The Stern-Gerlach Effect for Electrons* Herman Batelaan Gordon Gallup Julie Schwendiman TJG Behlen...
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Transcript of The Stern-Gerlach Effect for Electrons* Herman Batelaan Gordon Gallup Julie Schwendiman TJG Behlen...
The Stern-Gerlach Effect for Electrons
Herman BatelaanGordon Gallup
Julie SchwendimanTJG
Behlen Laboratory of PhysicsUniversity of Nebraska
Lincoln Nebraska 68588-0111
Work funded by the NSF ndash Physics Division
Electron Polarization
σρtrP spin
)N()N(
)N()N(PP
example
P = 03
65 spin-up
35 spin-down
Atomic Collisionsσ
cosθgfA
(from GDFletcher et alii PRA 31 2854 (1985))
Work done at NIST Gaithersburg by MRScheinfein et alii
RSI 61 2510 (1991)
From The Theory of Atomic Collisions NFMott and HSW Massey
-V
N
S
+V
Anti-Bohr Devices
a)
(Knauer)
b)
(Darwin)
N
c)
(Brillouin)
1930 Solvay Conference ndash ldquoLe Magnetismrdquo
See eg
bull Cohen-Tannoudji Diu et Laloeuml
bull Merzbacher
bull Mott amp Massey
bull Baym
bull Keβler
bull Ohanianhelliphelliphellip
I
Z
e-
Which ball arrives first A) high roadB) low roadC) simultaneously
z
H
x
H
0H
zx
y
Hz
Hx
vz
xe-
)1(Δv
v
x
z
z
H
x
H
0H
zx
y
CALCULATIONS
2
1
2
1
zyx
yxzB HiHH
iHHH
dt
di
spinEHvc
e
dt
pdF )(
eigenenergies
integrate
(spin-flip probability lt 10-3)
)( zyxHE Bspin
CHOOSE INITIAL CONDITIONS
2220 )()()( TvxTx
2)()( iie vxm
ei m
Txx
2)()( 0
require Δzspin ~ 1mm
use Bo = 10T a = 1 cm (iexcl105A)
rarr vz ~ 105 ms (30 meV)
rarr t ~ 10μs
rarr Δxi ~ 100 μm
20
2211
20 2)(
tantan2
ze
B
i
fiif
ze
Bspin vm
Ba
za
azz
a
z
a
z
vm
Baz
H Batelaan et al PRL 79 4518 (1997)
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
NB - The net acceleration of the (leading) spin-backward electrons is zero
B
Pauli Case
ΔrΔp ~ ħ2
Landau Case
ΔrΔp ~ ħ2
B
MAGNETIC BOTTLE FORCES
z
BμμF z
BLz
B F
BL
L
S
(always || )B
(always || )B
0z
Bz
eνz
ˆ
0Bz
Fully quantum-mechanical calculation
(field due to a current loop)
Landau Hamiltonian
bull KE
bull ~ -μLB
bull ~ -μBB
GAGallup et alii PRL 86 4508 (2001)
S
W
F = SW
Gedanken apparatus
~~ φ TDC
1m 104 turns 5A
2 cm bore 10T
APERTURES
10μm 1μm
106 Hz
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
- The Stern-Gerlach Effect for Electrons
- Electron Polarization
- Atomic Collisions
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- See eg
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- CALCULATIONS
- CHOOSE INITIAL CONDITIONS
- require Δzspin ~ 1mm use Bo = 10T a = 1 cm (iexcl105A) rarr vz ~ 105 ms (30 meV) rarr t ~ 10μs rarr Δxi ~ 100 μm
- Slide 25
- Slide 26
- Landau States
- Slide 28
- Slide 29
- Slide 30
- Fully quantum-mechanical calculation
- Slide 32
- Slide 33
- Slide 34
- Gedanken apparatus
- Slide 36
- Slide 37
- Conclusions
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Feasibility
-
Electron Polarization
σρtrP spin
)N()N(
)N()N(PP
example
P = 03
65 spin-up
35 spin-down
Atomic Collisionsσ
cosθgfA
(from GDFletcher et alii PRA 31 2854 (1985))
Work done at NIST Gaithersburg by MRScheinfein et alii
RSI 61 2510 (1991)
From The Theory of Atomic Collisions NFMott and HSW Massey
-V
N
S
+V
Anti-Bohr Devices
a)
(Knauer)
b)
(Darwin)
N
c)
(Brillouin)
1930 Solvay Conference ndash ldquoLe Magnetismrdquo
See eg
bull Cohen-Tannoudji Diu et Laloeuml
bull Merzbacher
bull Mott amp Massey
bull Baym
bull Keβler
bull Ohanianhelliphelliphellip
I
Z
e-
Which ball arrives first A) high roadB) low roadC) simultaneously
z
H
x
H
0H
zx
y
Hz
Hx
vz
xe-
)1(Δv
v
x
z
z
H
x
H
0H
zx
y
CALCULATIONS
2
1
2
1
zyx
yxzB HiHH
iHHH
dt
di
spinEHvc
e
dt
pdF )(
eigenenergies
integrate
(spin-flip probability lt 10-3)
)( zyxHE Bspin
CHOOSE INITIAL CONDITIONS
2220 )()()( TvxTx
2)()( iie vxm
ei m
Txx
2)()( 0
require Δzspin ~ 1mm
use Bo = 10T a = 1 cm (iexcl105A)
rarr vz ~ 105 ms (30 meV)
rarr t ~ 10μs
rarr Δxi ~ 100 μm
20
2211
20 2)(
tantan2
ze
B
i
fiif
ze
Bspin vm
Ba
za
azz
a
z
a
z
vm
Baz
H Batelaan et al PRL 79 4518 (1997)
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
NB - The net acceleration of the (leading) spin-backward electrons is zero
B
Pauli Case
ΔrΔp ~ ħ2
Landau Case
ΔrΔp ~ ħ2
B
MAGNETIC BOTTLE FORCES
z
BμμF z
BLz
B F
BL
L
S
(always || )B
(always || )B
0z
Bz
eνz
ˆ
0Bz
Fully quantum-mechanical calculation
(field due to a current loop)
Landau Hamiltonian
bull KE
bull ~ -μLB
bull ~ -μBB
GAGallup et alii PRL 86 4508 (2001)
S
W
F = SW
Gedanken apparatus
~~ φ TDC
1m 104 turns 5A
2 cm bore 10T
APERTURES
10μm 1μm
106 Hz
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
- The Stern-Gerlach Effect for Electrons
- Electron Polarization
- Atomic Collisions
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- See eg
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- CALCULATIONS
- CHOOSE INITIAL CONDITIONS
- require Δzspin ~ 1mm use Bo = 10T a = 1 cm (iexcl105A) rarr vz ~ 105 ms (30 meV) rarr t ~ 10μs rarr Δxi ~ 100 μm
- Slide 25
- Slide 26
- Landau States
- Slide 28
- Slide 29
- Slide 30
- Fully quantum-mechanical calculation
- Slide 32
- Slide 33
- Slide 34
- Gedanken apparatus
- Slide 36
- Slide 37
- Conclusions
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Feasibility
-
Atomic Collisionsσ
cosθgfA
(from GDFletcher et alii PRA 31 2854 (1985))
Work done at NIST Gaithersburg by MRScheinfein et alii
RSI 61 2510 (1991)
From The Theory of Atomic Collisions NFMott and HSW Massey
-V
N
S
+V
Anti-Bohr Devices
a)
(Knauer)
b)
(Darwin)
N
c)
(Brillouin)
1930 Solvay Conference ndash ldquoLe Magnetismrdquo
See eg
bull Cohen-Tannoudji Diu et Laloeuml
bull Merzbacher
bull Mott amp Massey
bull Baym
bull Keβler
bull Ohanianhelliphelliphellip
I
Z
e-
Which ball arrives first A) high roadB) low roadC) simultaneously
z
H
x
H
0H
zx
y
Hz
Hx
vz
xe-
)1(Δv
v
x
z
z
H
x
H
0H
zx
y
CALCULATIONS
2
1
2
1
zyx
yxzB HiHH
iHHH
dt
di
spinEHvc
e
dt
pdF )(
eigenenergies
integrate
(spin-flip probability lt 10-3)
)( zyxHE Bspin
CHOOSE INITIAL CONDITIONS
2220 )()()( TvxTx
2)()( iie vxm
ei m
Txx
2)()( 0
require Δzspin ~ 1mm
use Bo = 10T a = 1 cm (iexcl105A)
rarr vz ~ 105 ms (30 meV)
rarr t ~ 10μs
rarr Δxi ~ 100 μm
20
2211
20 2)(
tantan2
ze
B
i
fiif
ze
Bspin vm
Ba
za
azz
a
z
a
z
vm
Baz
H Batelaan et al PRL 79 4518 (1997)
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
NB - The net acceleration of the (leading) spin-backward electrons is zero
B
Pauli Case
ΔrΔp ~ ħ2
Landau Case
ΔrΔp ~ ħ2
B
MAGNETIC BOTTLE FORCES
z
BμμF z
BLz
B F
BL
L
S
(always || )B
(always || )B
0z
Bz
eνz
ˆ
0Bz
Fully quantum-mechanical calculation
(field due to a current loop)
Landau Hamiltonian
bull KE
bull ~ -μLB
bull ~ -μBB
GAGallup et alii PRL 86 4508 (2001)
S
W
F = SW
Gedanken apparatus
~~ φ TDC
1m 104 turns 5A
2 cm bore 10T
APERTURES
10μm 1μm
106 Hz
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
- The Stern-Gerlach Effect for Electrons
- Electron Polarization
- Atomic Collisions
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- See eg
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- CALCULATIONS
- CHOOSE INITIAL CONDITIONS
- require Δzspin ~ 1mm use Bo = 10T a = 1 cm (iexcl105A) rarr vz ~ 105 ms (30 meV) rarr t ~ 10μs rarr Δxi ~ 100 μm
- Slide 25
- Slide 26
- Landau States
- Slide 28
- Slide 29
- Slide 30
- Fully quantum-mechanical calculation
- Slide 32
- Slide 33
- Slide 34
- Gedanken apparatus
- Slide 36
- Slide 37
- Conclusions
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Feasibility
-
Work done at NIST Gaithersburg by MRScheinfein et alii
RSI 61 2510 (1991)
From The Theory of Atomic Collisions NFMott and HSW Massey
-V
N
S
+V
Anti-Bohr Devices
a)
(Knauer)
b)
(Darwin)
N
c)
(Brillouin)
1930 Solvay Conference ndash ldquoLe Magnetismrdquo
See eg
bull Cohen-Tannoudji Diu et Laloeuml
bull Merzbacher
bull Mott amp Massey
bull Baym
bull Keβler
bull Ohanianhelliphelliphellip
I
Z
e-
Which ball arrives first A) high roadB) low roadC) simultaneously
z
H
x
H
0H
zx
y
Hz
Hx
vz
xe-
)1(Δv
v
x
z
z
H
x
H
0H
zx
y
CALCULATIONS
2
1
2
1
zyx
yxzB HiHH
iHHH
dt
di
spinEHvc
e
dt
pdF )(
eigenenergies
integrate
(spin-flip probability lt 10-3)
)( zyxHE Bspin
CHOOSE INITIAL CONDITIONS
2220 )()()( TvxTx
2)()( iie vxm
ei m
Txx
2)()( 0
require Δzspin ~ 1mm
use Bo = 10T a = 1 cm (iexcl105A)
rarr vz ~ 105 ms (30 meV)
rarr t ~ 10μs
rarr Δxi ~ 100 μm
20
2211
20 2)(
tantan2
ze
B
i
fiif
ze
Bspin vm
Ba
za
azz
a
z
a
z
vm
Baz
H Batelaan et al PRL 79 4518 (1997)
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
NB - The net acceleration of the (leading) spin-backward electrons is zero
B
Pauli Case
ΔrΔp ~ ħ2
Landau Case
ΔrΔp ~ ħ2
B
MAGNETIC BOTTLE FORCES
z
BμμF z
BLz
B F
BL
L
S
(always || )B
(always || )B
0z
Bz
eνz
ˆ
0Bz
Fully quantum-mechanical calculation
(field due to a current loop)
Landau Hamiltonian
bull KE
bull ~ -μLB
bull ~ -μBB
GAGallup et alii PRL 86 4508 (2001)
S
W
F = SW
Gedanken apparatus
~~ φ TDC
1m 104 turns 5A
2 cm bore 10T
APERTURES
10μm 1μm
106 Hz
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
- The Stern-Gerlach Effect for Electrons
- Electron Polarization
- Atomic Collisions
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- See eg
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- CALCULATIONS
- CHOOSE INITIAL CONDITIONS
- require Δzspin ~ 1mm use Bo = 10T a = 1 cm (iexcl105A) rarr vz ~ 105 ms (30 meV) rarr t ~ 10μs rarr Δxi ~ 100 μm
- Slide 25
- Slide 26
- Landau States
- Slide 28
- Slide 29
- Slide 30
- Fully quantum-mechanical calculation
- Slide 32
- Slide 33
- Slide 34
- Gedanken apparatus
- Slide 36
- Slide 37
- Conclusions
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Feasibility
-
From The Theory of Atomic Collisions NFMott and HSW Massey
-V
N
S
+V
Anti-Bohr Devices
a)
(Knauer)
b)
(Darwin)
N
c)
(Brillouin)
1930 Solvay Conference ndash ldquoLe Magnetismrdquo
See eg
bull Cohen-Tannoudji Diu et Laloeuml
bull Merzbacher
bull Mott amp Massey
bull Baym
bull Keβler
bull Ohanianhelliphelliphellip
I
Z
e-
Which ball arrives first A) high roadB) low roadC) simultaneously
z
H
x
H
0H
zx
y
Hz
Hx
vz
xe-
)1(Δv
v
x
z
z
H
x
H
0H
zx
y
CALCULATIONS
2
1
2
1
zyx
yxzB HiHH
iHHH
dt
di
spinEHvc
e
dt
pdF )(
eigenenergies
integrate
(spin-flip probability lt 10-3)
)( zyxHE Bspin
CHOOSE INITIAL CONDITIONS
2220 )()()( TvxTx
2)()( iie vxm
ei m
Txx
2)()( 0
require Δzspin ~ 1mm
use Bo = 10T a = 1 cm (iexcl105A)
rarr vz ~ 105 ms (30 meV)
rarr t ~ 10μs
rarr Δxi ~ 100 μm
20
2211
20 2)(
tantan2
ze
B
i
fiif
ze
Bspin vm
Ba
za
azz
a
z
a
z
vm
Baz
H Batelaan et al PRL 79 4518 (1997)
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
NB - The net acceleration of the (leading) spin-backward electrons is zero
B
Pauli Case
ΔrΔp ~ ħ2
Landau Case
ΔrΔp ~ ħ2
B
MAGNETIC BOTTLE FORCES
z
BμμF z
BLz
B F
BL
L
S
(always || )B
(always || )B
0z
Bz
eνz
ˆ
0Bz
Fully quantum-mechanical calculation
(field due to a current loop)
Landau Hamiltonian
bull KE
bull ~ -μLB
bull ~ -μBB
GAGallup et alii PRL 86 4508 (2001)
S
W
F = SW
Gedanken apparatus
~~ φ TDC
1m 104 turns 5A
2 cm bore 10T
APERTURES
10μm 1μm
106 Hz
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
- The Stern-Gerlach Effect for Electrons
- Electron Polarization
- Atomic Collisions
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- See eg
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- CALCULATIONS
- CHOOSE INITIAL CONDITIONS
- require Δzspin ~ 1mm use Bo = 10T a = 1 cm (iexcl105A) rarr vz ~ 105 ms (30 meV) rarr t ~ 10μs rarr Δxi ~ 100 μm
- Slide 25
- Slide 26
- Landau States
- Slide 28
- Slide 29
- Slide 30
- Fully quantum-mechanical calculation
- Slide 32
- Slide 33
- Slide 34
- Gedanken apparatus
- Slide 36
- Slide 37
- Conclusions
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Feasibility
-
-V
N
S
+V
Anti-Bohr Devices
a)
(Knauer)
b)
(Darwin)
N
c)
(Brillouin)
1930 Solvay Conference ndash ldquoLe Magnetismrdquo
See eg
bull Cohen-Tannoudji Diu et Laloeuml
bull Merzbacher
bull Mott amp Massey
bull Baym
bull Keβler
bull Ohanianhelliphelliphellip
I
Z
e-
Which ball arrives first A) high roadB) low roadC) simultaneously
z
H
x
H
0H
zx
y
Hz
Hx
vz
xe-
)1(Δv
v
x
z
z
H
x
H
0H
zx
y
CALCULATIONS
2
1
2
1
zyx
yxzB HiHH
iHHH
dt
di
spinEHvc
e
dt
pdF )(
eigenenergies
integrate
(spin-flip probability lt 10-3)
)( zyxHE Bspin
CHOOSE INITIAL CONDITIONS
2220 )()()( TvxTx
2)()( iie vxm
ei m
Txx
2)()( 0
require Δzspin ~ 1mm
use Bo = 10T a = 1 cm (iexcl105A)
rarr vz ~ 105 ms (30 meV)
rarr t ~ 10μs
rarr Δxi ~ 100 μm
20
2211
20 2)(
tantan2
ze
B
i
fiif
ze
Bspin vm
Ba
za
azz
a
z
a
z
vm
Baz
H Batelaan et al PRL 79 4518 (1997)
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
NB - The net acceleration of the (leading) spin-backward electrons is zero
B
Pauli Case
ΔrΔp ~ ħ2
Landau Case
ΔrΔp ~ ħ2
B
MAGNETIC BOTTLE FORCES
z
BμμF z
BLz
B F
BL
L
S
(always || )B
(always || )B
0z
Bz
eνz
ˆ
0Bz
Fully quantum-mechanical calculation
(field due to a current loop)
Landau Hamiltonian
bull KE
bull ~ -μLB
bull ~ -μBB
GAGallup et alii PRL 86 4508 (2001)
S
W
F = SW
Gedanken apparatus
~~ φ TDC
1m 104 turns 5A
2 cm bore 10T
APERTURES
10μm 1μm
106 Hz
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
- The Stern-Gerlach Effect for Electrons
- Electron Polarization
- Atomic Collisions
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- See eg
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- CALCULATIONS
- CHOOSE INITIAL CONDITIONS
- require Δzspin ~ 1mm use Bo = 10T a = 1 cm (iexcl105A) rarr vz ~ 105 ms (30 meV) rarr t ~ 10μs rarr Δxi ~ 100 μm
- Slide 25
- Slide 26
- Landau States
- Slide 28
- Slide 29
- Slide 30
- Fully quantum-mechanical calculation
- Slide 32
- Slide 33
- Slide 34
- Gedanken apparatus
- Slide 36
- Slide 37
- Conclusions
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Feasibility
-
b)
(Darwin)
N
c)
(Brillouin)
1930 Solvay Conference ndash ldquoLe Magnetismrdquo
See eg
bull Cohen-Tannoudji Diu et Laloeuml
bull Merzbacher
bull Mott amp Massey
bull Baym
bull Keβler
bull Ohanianhelliphelliphellip
I
Z
e-
Which ball arrives first A) high roadB) low roadC) simultaneously
z
H
x
H
0H
zx
y
Hz
Hx
vz
xe-
)1(Δv
v
x
z
z
H
x
H
0H
zx
y
CALCULATIONS
2
1
2
1
zyx
yxzB HiHH
iHHH
dt
di
spinEHvc
e
dt
pdF )(
eigenenergies
integrate
(spin-flip probability lt 10-3)
)( zyxHE Bspin
CHOOSE INITIAL CONDITIONS
2220 )()()( TvxTx
2)()( iie vxm
ei m
Txx
2)()( 0
require Δzspin ~ 1mm
use Bo = 10T a = 1 cm (iexcl105A)
rarr vz ~ 105 ms (30 meV)
rarr t ~ 10μs
rarr Δxi ~ 100 μm
20
2211
20 2)(
tantan2
ze
B
i
fiif
ze
Bspin vm
Ba
za
azz
a
z
a
z
vm
Baz
H Batelaan et al PRL 79 4518 (1997)
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
NB - The net acceleration of the (leading) spin-backward electrons is zero
B
Pauli Case
ΔrΔp ~ ħ2
Landau Case
ΔrΔp ~ ħ2
B
MAGNETIC BOTTLE FORCES
z
BμμF z
BLz
B F
BL
L
S
(always || )B
(always || )B
0z
Bz
eνz
ˆ
0Bz
Fully quantum-mechanical calculation
(field due to a current loop)
Landau Hamiltonian
bull KE
bull ~ -μLB
bull ~ -μBB
GAGallup et alii PRL 86 4508 (2001)
S
W
F = SW
Gedanken apparatus
~~ φ TDC
1m 104 turns 5A
2 cm bore 10T
APERTURES
10μm 1μm
106 Hz
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
- The Stern-Gerlach Effect for Electrons
- Electron Polarization
- Atomic Collisions
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- See eg
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- CALCULATIONS
- CHOOSE INITIAL CONDITIONS
- require Δzspin ~ 1mm use Bo = 10T a = 1 cm (iexcl105A) rarr vz ~ 105 ms (30 meV) rarr t ~ 10μs rarr Δxi ~ 100 μm
- Slide 25
- Slide 26
- Landau States
- Slide 28
- Slide 29
- Slide 30
- Fully quantum-mechanical calculation
- Slide 32
- Slide 33
- Slide 34
- Gedanken apparatus
- Slide 36
- Slide 37
- Conclusions
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Feasibility
-
N
c)
(Brillouin)
1930 Solvay Conference ndash ldquoLe Magnetismrdquo
See eg
bull Cohen-Tannoudji Diu et Laloeuml
bull Merzbacher
bull Mott amp Massey
bull Baym
bull Keβler
bull Ohanianhelliphelliphellip
I
Z
e-
Which ball arrives first A) high roadB) low roadC) simultaneously
z
H
x
H
0H
zx
y
Hz
Hx
vz
xe-
)1(Δv
v
x
z
z
H
x
H
0H
zx
y
CALCULATIONS
2
1
2
1
zyx
yxzB HiHH
iHHH
dt
di
spinEHvc
e
dt
pdF )(
eigenenergies
integrate
(spin-flip probability lt 10-3)
)( zyxHE Bspin
CHOOSE INITIAL CONDITIONS
2220 )()()( TvxTx
2)()( iie vxm
ei m
Txx
2)()( 0
require Δzspin ~ 1mm
use Bo = 10T a = 1 cm (iexcl105A)
rarr vz ~ 105 ms (30 meV)
rarr t ~ 10μs
rarr Δxi ~ 100 μm
20
2211
20 2)(
tantan2
ze
B
i
fiif
ze
Bspin vm
Ba
za
azz
a
z
a
z
vm
Baz
H Batelaan et al PRL 79 4518 (1997)
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
NB - The net acceleration of the (leading) spin-backward electrons is zero
B
Pauli Case
ΔrΔp ~ ħ2
Landau Case
ΔrΔp ~ ħ2
B
MAGNETIC BOTTLE FORCES
z
BμμF z
BLz
B F
BL
L
S
(always || )B
(always || )B
0z
Bz
eνz
ˆ
0Bz
Fully quantum-mechanical calculation
(field due to a current loop)
Landau Hamiltonian
bull KE
bull ~ -μLB
bull ~ -μBB
GAGallup et alii PRL 86 4508 (2001)
S
W
F = SW
Gedanken apparatus
~~ φ TDC
1m 104 turns 5A
2 cm bore 10T
APERTURES
10μm 1μm
106 Hz
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
- The Stern-Gerlach Effect for Electrons
- Electron Polarization
- Atomic Collisions
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- See eg
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- CALCULATIONS
- CHOOSE INITIAL CONDITIONS
- require Δzspin ~ 1mm use Bo = 10T a = 1 cm (iexcl105A) rarr vz ~ 105 ms (30 meV) rarr t ~ 10μs rarr Δxi ~ 100 μm
- Slide 25
- Slide 26
- Landau States
- Slide 28
- Slide 29
- Slide 30
- Fully quantum-mechanical calculation
- Slide 32
- Slide 33
- Slide 34
- Gedanken apparatus
- Slide 36
- Slide 37
- Conclusions
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Feasibility
-
1930 Solvay Conference ndash ldquoLe Magnetismrdquo
See eg
bull Cohen-Tannoudji Diu et Laloeuml
bull Merzbacher
bull Mott amp Massey
bull Baym
bull Keβler
bull Ohanianhelliphelliphellip
I
Z
e-
Which ball arrives first A) high roadB) low roadC) simultaneously
z
H
x
H
0H
zx
y
Hz
Hx
vz
xe-
)1(Δv
v
x
z
z
H
x
H
0H
zx
y
CALCULATIONS
2
1
2
1
zyx
yxzB HiHH
iHHH
dt
di
spinEHvc
e
dt
pdF )(
eigenenergies
integrate
(spin-flip probability lt 10-3)
)( zyxHE Bspin
CHOOSE INITIAL CONDITIONS
2220 )()()( TvxTx
2)()( iie vxm
ei m
Txx
2)()( 0
require Δzspin ~ 1mm
use Bo = 10T a = 1 cm (iexcl105A)
rarr vz ~ 105 ms (30 meV)
rarr t ~ 10μs
rarr Δxi ~ 100 μm
20
2211
20 2)(
tantan2
ze
B
i
fiif
ze
Bspin vm
Ba
za
azz
a
z
a
z
vm
Baz
H Batelaan et al PRL 79 4518 (1997)
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
NB - The net acceleration of the (leading) spin-backward electrons is zero
B
Pauli Case
ΔrΔp ~ ħ2
Landau Case
ΔrΔp ~ ħ2
B
MAGNETIC BOTTLE FORCES
z
BμμF z
BLz
B F
BL
L
S
(always || )B
(always || )B
0z
Bz
eνz
ˆ
0Bz
Fully quantum-mechanical calculation
(field due to a current loop)
Landau Hamiltonian
bull KE
bull ~ -μLB
bull ~ -μBB
GAGallup et alii PRL 86 4508 (2001)
S
W
F = SW
Gedanken apparatus
~~ φ TDC
1m 104 turns 5A
2 cm bore 10T
APERTURES
10μm 1μm
106 Hz
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
- The Stern-Gerlach Effect for Electrons
- Electron Polarization
- Atomic Collisions
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- See eg
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- CALCULATIONS
- CHOOSE INITIAL CONDITIONS
- require Δzspin ~ 1mm use Bo = 10T a = 1 cm (iexcl105A) rarr vz ~ 105 ms (30 meV) rarr t ~ 10μs rarr Δxi ~ 100 μm
- Slide 25
- Slide 26
- Landau States
- Slide 28
- Slide 29
- Slide 30
- Fully quantum-mechanical calculation
- Slide 32
- Slide 33
- Slide 34
- Gedanken apparatus
- Slide 36
- Slide 37
- Conclusions
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Feasibility
-
See eg
bull Cohen-Tannoudji Diu et Laloeuml
bull Merzbacher
bull Mott amp Massey
bull Baym
bull Keβler
bull Ohanianhelliphelliphellip
I
Z
e-
Which ball arrives first A) high roadB) low roadC) simultaneously
z
H
x
H
0H
zx
y
Hz
Hx
vz
xe-
)1(Δv
v
x
z
z
H
x
H
0H
zx
y
CALCULATIONS
2
1
2
1
zyx
yxzB HiHH
iHHH
dt
di
spinEHvc
e
dt
pdF )(
eigenenergies
integrate
(spin-flip probability lt 10-3)
)( zyxHE Bspin
CHOOSE INITIAL CONDITIONS
2220 )()()( TvxTx
2)()( iie vxm
ei m
Txx
2)()( 0
require Δzspin ~ 1mm
use Bo = 10T a = 1 cm (iexcl105A)
rarr vz ~ 105 ms (30 meV)
rarr t ~ 10μs
rarr Δxi ~ 100 μm
20
2211
20 2)(
tantan2
ze
B
i
fiif
ze
Bspin vm
Ba
za
azz
a
z
a
z
vm
Baz
H Batelaan et al PRL 79 4518 (1997)
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
NB - The net acceleration of the (leading) spin-backward electrons is zero
B
Pauli Case
ΔrΔp ~ ħ2
Landau Case
ΔrΔp ~ ħ2
B
MAGNETIC BOTTLE FORCES
z
BμμF z
BLz
B F
BL
L
S
(always || )B
(always || )B
0z
Bz
eνz
ˆ
0Bz
Fully quantum-mechanical calculation
(field due to a current loop)
Landau Hamiltonian
bull KE
bull ~ -μLB
bull ~ -μBB
GAGallup et alii PRL 86 4508 (2001)
S
W
F = SW
Gedanken apparatus
~~ φ TDC
1m 104 turns 5A
2 cm bore 10T
APERTURES
10μm 1μm
106 Hz
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
- The Stern-Gerlach Effect for Electrons
- Electron Polarization
- Atomic Collisions
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- See eg
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- CALCULATIONS
- CHOOSE INITIAL CONDITIONS
- require Δzspin ~ 1mm use Bo = 10T a = 1 cm (iexcl105A) rarr vz ~ 105 ms (30 meV) rarr t ~ 10μs rarr Δxi ~ 100 μm
- Slide 25
- Slide 26
- Landau States
- Slide 28
- Slide 29
- Slide 30
- Fully quantum-mechanical calculation
- Slide 32
- Slide 33
- Slide 34
- Gedanken apparatus
- Slide 36
- Slide 37
- Conclusions
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Feasibility
-
I
Z
e-
Which ball arrives first A) high roadB) low roadC) simultaneously
z
H
x
H
0H
zx
y
Hz
Hx
vz
xe-
)1(Δv
v
x
z
z
H
x
H
0H
zx
y
CALCULATIONS
2
1
2
1
zyx
yxzB HiHH
iHHH
dt
di
spinEHvc
e
dt
pdF )(
eigenenergies
integrate
(spin-flip probability lt 10-3)
)( zyxHE Bspin
CHOOSE INITIAL CONDITIONS
2220 )()()( TvxTx
2)()( iie vxm
ei m
Txx
2)()( 0
require Δzspin ~ 1mm
use Bo = 10T a = 1 cm (iexcl105A)
rarr vz ~ 105 ms (30 meV)
rarr t ~ 10μs
rarr Δxi ~ 100 μm
20
2211
20 2)(
tantan2
ze
B
i
fiif
ze
Bspin vm
Ba
za
azz
a
z
a
z
vm
Baz
H Batelaan et al PRL 79 4518 (1997)
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
NB - The net acceleration of the (leading) spin-backward electrons is zero
B
Pauli Case
ΔrΔp ~ ħ2
Landau Case
ΔrΔp ~ ħ2
B
MAGNETIC BOTTLE FORCES
z
BμμF z
BLz
B F
BL
L
S
(always || )B
(always || )B
0z
Bz
eνz
ˆ
0Bz
Fully quantum-mechanical calculation
(field due to a current loop)
Landau Hamiltonian
bull KE
bull ~ -μLB
bull ~ -μBB
GAGallup et alii PRL 86 4508 (2001)
S
W
F = SW
Gedanken apparatus
~~ φ TDC
1m 104 turns 5A
2 cm bore 10T
APERTURES
10μm 1μm
106 Hz
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
- The Stern-Gerlach Effect for Electrons
- Electron Polarization
- Atomic Collisions
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- See eg
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- CALCULATIONS
- CHOOSE INITIAL CONDITIONS
- require Δzspin ~ 1mm use Bo = 10T a = 1 cm (iexcl105A) rarr vz ~ 105 ms (30 meV) rarr t ~ 10μs rarr Δxi ~ 100 μm
- Slide 25
- Slide 26
- Landau States
- Slide 28
- Slide 29
- Slide 30
- Fully quantum-mechanical calculation
- Slide 32
- Slide 33
- Slide 34
- Gedanken apparatus
- Slide 36
- Slide 37
- Conclusions
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Feasibility
-
Which ball arrives first A) high roadB) low roadC) simultaneously
z
H
x
H
0H
zx
y
Hz
Hx
vz
xe-
)1(Δv
v
x
z
z
H
x
H
0H
zx
y
CALCULATIONS
2
1
2
1
zyx
yxzB HiHH
iHHH
dt
di
spinEHvc
e
dt
pdF )(
eigenenergies
integrate
(spin-flip probability lt 10-3)
)( zyxHE Bspin
CHOOSE INITIAL CONDITIONS
2220 )()()( TvxTx
2)()( iie vxm
ei m
Txx
2)()( 0
require Δzspin ~ 1mm
use Bo = 10T a = 1 cm (iexcl105A)
rarr vz ~ 105 ms (30 meV)
rarr t ~ 10μs
rarr Δxi ~ 100 μm
20
2211
20 2)(
tantan2
ze
B
i
fiif
ze
Bspin vm
Ba
za
azz
a
z
a
z
vm
Baz
H Batelaan et al PRL 79 4518 (1997)
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
NB - The net acceleration of the (leading) spin-backward electrons is zero
B
Pauli Case
ΔrΔp ~ ħ2
Landau Case
ΔrΔp ~ ħ2
B
MAGNETIC BOTTLE FORCES
z
BμμF z
BLz
B F
BL
L
S
(always || )B
(always || )B
0z
Bz
eνz
ˆ
0Bz
Fully quantum-mechanical calculation
(field due to a current loop)
Landau Hamiltonian
bull KE
bull ~ -μLB
bull ~ -μBB
GAGallup et alii PRL 86 4508 (2001)
S
W
F = SW
Gedanken apparatus
~~ φ TDC
1m 104 turns 5A
2 cm bore 10T
APERTURES
10μm 1μm
106 Hz
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
- The Stern-Gerlach Effect for Electrons
- Electron Polarization
- Atomic Collisions
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- See eg
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- CALCULATIONS
- CHOOSE INITIAL CONDITIONS
- require Δzspin ~ 1mm use Bo = 10T a = 1 cm (iexcl105A) rarr vz ~ 105 ms (30 meV) rarr t ~ 10μs rarr Δxi ~ 100 μm
- Slide 25
- Slide 26
- Landau States
- Slide 28
- Slide 29
- Slide 30
- Fully quantum-mechanical calculation
- Slide 32
- Slide 33
- Slide 34
- Gedanken apparatus
- Slide 36
- Slide 37
- Conclusions
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Feasibility
-
z
H
x
H
0H
zx
y
Hz
Hx
vz
xe-
)1(Δv
v
x
z
z
H
x
H
0H
zx
y
CALCULATIONS
2
1
2
1
zyx
yxzB HiHH
iHHH
dt
di
spinEHvc
e
dt
pdF )(
eigenenergies
integrate
(spin-flip probability lt 10-3)
)( zyxHE Bspin
CHOOSE INITIAL CONDITIONS
2220 )()()( TvxTx
2)()( iie vxm
ei m
Txx
2)()( 0
require Δzspin ~ 1mm
use Bo = 10T a = 1 cm (iexcl105A)
rarr vz ~ 105 ms (30 meV)
rarr t ~ 10μs
rarr Δxi ~ 100 μm
20
2211
20 2)(
tantan2
ze
B
i
fiif
ze
Bspin vm
Ba
za
azz
a
z
a
z
vm
Baz
H Batelaan et al PRL 79 4518 (1997)
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
NB - The net acceleration of the (leading) spin-backward electrons is zero
B
Pauli Case
ΔrΔp ~ ħ2
Landau Case
ΔrΔp ~ ħ2
B
MAGNETIC BOTTLE FORCES
z
BμμF z
BLz
B F
BL
L
S
(always || )B
(always || )B
0z
Bz
eνz
ˆ
0Bz
Fully quantum-mechanical calculation
(field due to a current loop)
Landau Hamiltonian
bull KE
bull ~ -μLB
bull ~ -μBB
GAGallup et alii PRL 86 4508 (2001)
S
W
F = SW
Gedanken apparatus
~~ φ TDC
1m 104 turns 5A
2 cm bore 10T
APERTURES
10μm 1μm
106 Hz
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
- The Stern-Gerlach Effect for Electrons
- Electron Polarization
- Atomic Collisions
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- See eg
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- CALCULATIONS
- CHOOSE INITIAL CONDITIONS
- require Δzspin ~ 1mm use Bo = 10T a = 1 cm (iexcl105A) rarr vz ~ 105 ms (30 meV) rarr t ~ 10μs rarr Δxi ~ 100 μm
- Slide 25
- Slide 26
- Landau States
- Slide 28
- Slide 29
- Slide 30
- Fully quantum-mechanical calculation
- Slide 32
- Slide 33
- Slide 34
- Gedanken apparatus
- Slide 36
- Slide 37
- Conclusions
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Feasibility
-
CALCULATIONS
2
1
2
1
zyx
yxzB HiHH
iHHH
dt
di
spinEHvc
e
dt
pdF )(
eigenenergies
integrate
(spin-flip probability lt 10-3)
)( zyxHE Bspin
CHOOSE INITIAL CONDITIONS
2220 )()()( TvxTx
2)()( iie vxm
ei m
Txx
2)()( 0
require Δzspin ~ 1mm
use Bo = 10T a = 1 cm (iexcl105A)
rarr vz ~ 105 ms (30 meV)
rarr t ~ 10μs
rarr Δxi ~ 100 μm
20
2211
20 2)(
tantan2
ze
B
i
fiif
ze
Bspin vm
Ba
za
azz
a
z
a
z
vm
Baz
H Batelaan et al PRL 79 4518 (1997)
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
NB - The net acceleration of the (leading) spin-backward electrons is zero
B
Pauli Case
ΔrΔp ~ ħ2
Landau Case
ΔrΔp ~ ħ2
B
MAGNETIC BOTTLE FORCES
z
BμμF z
BLz
B F
BL
L
S
(always || )B
(always || )B
0z
Bz
eνz
ˆ
0Bz
Fully quantum-mechanical calculation
(field due to a current loop)
Landau Hamiltonian
bull KE
bull ~ -μLB
bull ~ -μBB
GAGallup et alii PRL 86 4508 (2001)
S
W
F = SW
Gedanken apparatus
~~ φ TDC
1m 104 turns 5A
2 cm bore 10T
APERTURES
10μm 1μm
106 Hz
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
- The Stern-Gerlach Effect for Electrons
- Electron Polarization
- Atomic Collisions
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- See eg
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- CALCULATIONS
- CHOOSE INITIAL CONDITIONS
- require Δzspin ~ 1mm use Bo = 10T a = 1 cm (iexcl105A) rarr vz ~ 105 ms (30 meV) rarr t ~ 10μs rarr Δxi ~ 100 μm
- Slide 25
- Slide 26
- Landau States
- Slide 28
- Slide 29
- Slide 30
- Fully quantum-mechanical calculation
- Slide 32
- Slide 33
- Slide 34
- Gedanken apparatus
- Slide 36
- Slide 37
- Conclusions
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Feasibility
-
CHOOSE INITIAL CONDITIONS
2220 )()()( TvxTx
2)()( iie vxm
ei m
Txx
2)()( 0
require Δzspin ~ 1mm
use Bo = 10T a = 1 cm (iexcl105A)
rarr vz ~ 105 ms (30 meV)
rarr t ~ 10μs
rarr Δxi ~ 100 μm
20
2211
20 2)(
tantan2
ze
B
i
fiif
ze
Bspin vm
Ba
za
azz
a
z
a
z
vm
Baz
H Batelaan et al PRL 79 4518 (1997)
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
NB - The net acceleration of the (leading) spin-backward electrons is zero
B
Pauli Case
ΔrΔp ~ ħ2
Landau Case
ΔrΔp ~ ħ2
B
MAGNETIC BOTTLE FORCES
z
BμμF z
BLz
B F
BL
L
S
(always || )B
(always || )B
0z
Bz
eνz
ˆ
0Bz
Fully quantum-mechanical calculation
(field due to a current loop)
Landau Hamiltonian
bull KE
bull ~ -μLB
bull ~ -μBB
GAGallup et alii PRL 86 4508 (2001)
S
W
F = SW
Gedanken apparatus
~~ φ TDC
1m 104 turns 5A
2 cm bore 10T
APERTURES
10μm 1μm
106 Hz
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
- The Stern-Gerlach Effect for Electrons
- Electron Polarization
- Atomic Collisions
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- See eg
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- CALCULATIONS
- CHOOSE INITIAL CONDITIONS
- require Δzspin ~ 1mm use Bo = 10T a = 1 cm (iexcl105A) rarr vz ~ 105 ms (30 meV) rarr t ~ 10μs rarr Δxi ~ 100 μm
- Slide 25
- Slide 26
- Landau States
- Slide 28
- Slide 29
- Slide 30
- Fully quantum-mechanical calculation
- Slide 32
- Slide 33
- Slide 34
- Gedanken apparatus
- Slide 36
- Slide 37
- Conclusions
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Feasibility
-
require Δzspin ~ 1mm
use Bo = 10T a = 1 cm (iexcl105A)
rarr vz ~ 105 ms (30 meV)
rarr t ~ 10μs
rarr Δxi ~ 100 μm
20
2211
20 2)(
tantan2
ze
B
i
fiif
ze
Bspin vm
Ba
za
azz
a
z
a
z
vm
Baz
H Batelaan et al PRL 79 4518 (1997)
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
NB - The net acceleration of the (leading) spin-backward electrons is zero
B
Pauli Case
ΔrΔp ~ ħ2
Landau Case
ΔrΔp ~ ħ2
B
MAGNETIC BOTTLE FORCES
z
BμμF z
BLz
B F
BL
L
S
(always || )B
(always || )B
0z
Bz
eνz
ˆ
0Bz
Fully quantum-mechanical calculation
(field due to a current loop)
Landau Hamiltonian
bull KE
bull ~ -μLB
bull ~ -μBB
GAGallup et alii PRL 86 4508 (2001)
S
W
F = SW
Gedanken apparatus
~~ φ TDC
1m 104 turns 5A
2 cm bore 10T
APERTURES
10μm 1μm
106 Hz
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
- The Stern-Gerlach Effect for Electrons
- Electron Polarization
- Atomic Collisions
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- See eg
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- CALCULATIONS
- CHOOSE INITIAL CONDITIONS
- require Δzspin ~ 1mm use Bo = 10T a = 1 cm (iexcl105A) rarr vz ~ 105 ms (30 meV) rarr t ~ 10μs rarr Δxi ~ 100 μm
- Slide 25
- Slide 26
- Landau States
- Slide 28
- Slide 29
- Slide 30
- Fully quantum-mechanical calculation
- Slide 32
- Slide 33
- Slide 34
- Gedanken apparatus
- Slide 36
- Slide 37
- Conclusions
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Feasibility
-
H Batelaan et al PRL 79 4518 (1997)
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
NB - The net acceleration of the (leading) spin-backward electrons is zero
B
Pauli Case
ΔrΔp ~ ħ2
Landau Case
ΔrΔp ~ ħ2
B
MAGNETIC BOTTLE FORCES
z
BμμF z
BLz
B F
BL
L
S
(always || )B
(always || )B
0z
Bz
eνz
ˆ
0Bz
Fully quantum-mechanical calculation
(field due to a current loop)
Landau Hamiltonian
bull KE
bull ~ -μLB
bull ~ -μBB
GAGallup et alii PRL 86 4508 (2001)
S
W
F = SW
Gedanken apparatus
~~ φ TDC
1m 104 turns 5A
2 cm bore 10T
APERTURES
10μm 1μm
106 Hz
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
- The Stern-Gerlach Effect for Electrons
- Electron Polarization
- Atomic Collisions
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- See eg
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- CALCULATIONS
- CHOOSE INITIAL CONDITIONS
- require Δzspin ~ 1mm use Bo = 10T a = 1 cm (iexcl105A) rarr vz ~ 105 ms (30 meV) rarr t ~ 10μs rarr Δxi ~ 100 μm
- Slide 25
- Slide 26
- Landau States
- Slide 28
- Slide 29
- Slide 30
- Fully quantum-mechanical calculation
- Slide 32
- Slide 33
- Slide 34
- Gedanken apparatus
- Slide 36
- Slide 37
- Conclusions
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Feasibility
-
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
NB - The net acceleration of the (leading) spin-backward electrons is zero
B
Pauli Case
ΔrΔp ~ ħ2
Landau Case
ΔrΔp ~ ħ2
B
MAGNETIC BOTTLE FORCES
z
BμμF z
BLz
B F
BL
L
S
(always || )B
(always || )B
0z
Bz
eνz
ˆ
0Bz
Fully quantum-mechanical calculation
(field due to a current loop)
Landau Hamiltonian
bull KE
bull ~ -μLB
bull ~ -μBB
GAGallup et alii PRL 86 4508 (2001)
S
W
F = SW
Gedanken apparatus
~~ φ TDC
1m 104 turns 5A
2 cm bore 10T
APERTURES
10μm 1μm
106 Hz
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
- The Stern-Gerlach Effect for Electrons
- Electron Polarization
- Atomic Collisions
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- See eg
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- CALCULATIONS
- CHOOSE INITIAL CONDITIONS
- require Δzspin ~ 1mm use Bo = 10T a = 1 cm (iexcl105A) rarr vz ~ 105 ms (30 meV) rarr t ~ 10μs rarr Δxi ~ 100 μm
- Slide 25
- Slide 26
- Landau States
- Slide 28
- Slide 29
- Slide 30
- Fully quantum-mechanical calculation
- Slide 32
- Slide 33
- Slide 34
- Gedanken apparatus
- Slide 36
- Slide 37
- Conclusions
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Feasibility
-
NB - The net acceleration of the (leading) spin-backward electrons is zero
B
Pauli Case
ΔrΔp ~ ħ2
Landau Case
ΔrΔp ~ ħ2
B
MAGNETIC BOTTLE FORCES
z
BμμF z
BLz
B F
BL
L
S
(always || )B
(always || )B
0z
Bz
eνz
ˆ
0Bz
Fully quantum-mechanical calculation
(field due to a current loop)
Landau Hamiltonian
bull KE
bull ~ -μLB
bull ~ -μBB
GAGallup et alii PRL 86 4508 (2001)
S
W
F = SW
Gedanken apparatus
~~ φ TDC
1m 104 turns 5A
2 cm bore 10T
APERTURES
10μm 1μm
106 Hz
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
- The Stern-Gerlach Effect for Electrons
- Electron Polarization
- Atomic Collisions
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- See eg
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- CALCULATIONS
- CHOOSE INITIAL CONDITIONS
- require Δzspin ~ 1mm use Bo = 10T a = 1 cm (iexcl105A) rarr vz ~ 105 ms (30 meV) rarr t ~ 10μs rarr Δxi ~ 100 μm
- Slide 25
- Slide 26
- Landau States
- Slide 28
- Slide 29
- Slide 30
- Fully quantum-mechanical calculation
- Slide 32
- Slide 33
- Slide 34
- Gedanken apparatus
- Slide 36
- Slide 37
- Conclusions
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Feasibility
-
B
Pauli Case
ΔrΔp ~ ħ2
Landau Case
ΔrΔp ~ ħ2
B
MAGNETIC BOTTLE FORCES
z
BμμF z
BLz
B F
BL
L
S
(always || )B
(always || )B
0z
Bz
eνz
ˆ
0Bz
Fully quantum-mechanical calculation
(field due to a current loop)
Landau Hamiltonian
bull KE
bull ~ -μLB
bull ~ -μBB
GAGallup et alii PRL 86 4508 (2001)
S
W
F = SW
Gedanken apparatus
~~ φ TDC
1m 104 turns 5A
2 cm bore 10T
APERTURES
10μm 1μm
106 Hz
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
- The Stern-Gerlach Effect for Electrons
- Electron Polarization
- Atomic Collisions
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- See eg
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- CALCULATIONS
- CHOOSE INITIAL CONDITIONS
- require Δzspin ~ 1mm use Bo = 10T a = 1 cm (iexcl105A) rarr vz ~ 105 ms (30 meV) rarr t ~ 10μs rarr Δxi ~ 100 μm
- Slide 25
- Slide 26
- Landau States
- Slide 28
- Slide 29
- Slide 30
- Fully quantum-mechanical calculation
- Slide 32
- Slide 33
- Slide 34
- Gedanken apparatus
- Slide 36
- Slide 37
- Conclusions
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Feasibility
-
MAGNETIC BOTTLE FORCES
z
BμμF z
BLz
B F
BL
L
S
(always || )B
(always || )B
0z
Bz
eνz
ˆ
0Bz
Fully quantum-mechanical calculation
(field due to a current loop)
Landau Hamiltonian
bull KE
bull ~ -μLB
bull ~ -μBB
GAGallup et alii PRL 86 4508 (2001)
S
W
F = SW
Gedanken apparatus
~~ φ TDC
1m 104 turns 5A
2 cm bore 10T
APERTURES
10μm 1μm
106 Hz
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
- The Stern-Gerlach Effect for Electrons
- Electron Polarization
- Atomic Collisions
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- See eg
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- CALCULATIONS
- CHOOSE INITIAL CONDITIONS
- require Δzspin ~ 1mm use Bo = 10T a = 1 cm (iexcl105A) rarr vz ~ 105 ms (30 meV) rarr t ~ 10μs rarr Δxi ~ 100 μm
- Slide 25
- Slide 26
- Landau States
- Slide 28
- Slide 29
- Slide 30
- Fully quantum-mechanical calculation
- Slide 32
- Slide 33
- Slide 34
- Gedanken apparatus
- Slide 36
- Slide 37
- Conclusions
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Feasibility
-
Fully quantum-mechanical calculation
(field due to a current loop)
Landau Hamiltonian
bull KE
bull ~ -μLB
bull ~ -μBB
GAGallup et alii PRL 86 4508 (2001)
S
W
F = SW
Gedanken apparatus
~~ φ TDC
1m 104 turns 5A
2 cm bore 10T
APERTURES
10μm 1μm
106 Hz
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
- The Stern-Gerlach Effect for Electrons
- Electron Polarization
- Atomic Collisions
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- See eg
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- CALCULATIONS
- CHOOSE INITIAL CONDITIONS
- require Δzspin ~ 1mm use Bo = 10T a = 1 cm (iexcl105A) rarr vz ~ 105 ms (30 meV) rarr t ~ 10μs rarr Δxi ~ 100 μm
- Slide 25
- Slide 26
- Landau States
- Slide 28
- Slide 29
- Slide 30
- Fully quantum-mechanical calculation
- Slide 32
- Slide 33
- Slide 34
- Gedanken apparatus
- Slide 36
- Slide 37
- Conclusions
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Feasibility
-
GAGallup et alii PRL 86 4508 (2001)
S
W
F = SW
Gedanken apparatus
~~ φ TDC
1m 104 turns 5A
2 cm bore 10T
APERTURES
10μm 1μm
106 Hz
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
- The Stern-Gerlach Effect for Electrons
- Electron Polarization
- Atomic Collisions
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- See eg
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- CALCULATIONS
- CHOOSE INITIAL CONDITIONS
- require Δzspin ~ 1mm use Bo = 10T a = 1 cm (iexcl105A) rarr vz ~ 105 ms (30 meV) rarr t ~ 10μs rarr Δxi ~ 100 μm
- Slide 25
- Slide 26
- Landau States
- Slide 28
- Slide 29
- Slide 30
- Fully quantum-mechanical calculation
- Slide 32
- Slide 33
- Slide 34
- Gedanken apparatus
- Slide 36
- Slide 37
- Conclusions
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Feasibility
-
S
W
F = SW
Gedanken apparatus
~~ φ TDC
1m 104 turns 5A
2 cm bore 10T
APERTURES
10μm 1μm
106 Hz
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
- The Stern-Gerlach Effect for Electrons
- Electron Polarization
- Atomic Collisions
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- See eg
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- CALCULATIONS
- CHOOSE INITIAL CONDITIONS
- require Δzspin ~ 1mm use Bo = 10T a = 1 cm (iexcl105A) rarr vz ~ 105 ms (30 meV) rarr t ~ 10μs rarr Δxi ~ 100 μm
- Slide 25
- Slide 26
- Landau States
- Slide 28
- Slide 29
- Slide 30
- Fully quantum-mechanical calculation
- Slide 32
- Slide 33
- Slide 34
- Gedanken apparatus
- Slide 36
- Slide 37
- Conclusions
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Feasibility
-
Gedanken apparatus
~~ φ TDC
1m 104 turns 5A
2 cm bore 10T
APERTURES
10μm 1μm
106 Hz
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
- The Stern-Gerlach Effect for Electrons
- Electron Polarization
- Atomic Collisions
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- See eg
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- CALCULATIONS
- CHOOSE INITIAL CONDITIONS
- require Δzspin ~ 1mm use Bo = 10T a = 1 cm (iexcl105A) rarr vz ~ 105 ms (30 meV) rarr t ~ 10μs rarr Δxi ~ 100 μm
- Slide 25
- Slide 26
- Landau States
- Slide 28
- Slide 29
- Slide 30
- Fully quantum-mechanical calculation
- Slide 32
- Slide 33
- Slide 34
- Gedanken apparatus
- Slide 36
- Slide 37
- Conclusions
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Feasibility
-
Landau States
0 +12
1 -12
0 -12
1 +12
2 -12
(n ms)E-(pz
22m)
0
En = (pz22m) + (2n + 1)μBB plusmn μBB
n = (0123hellip)
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
- The Stern-Gerlach Effect for Electrons
- Electron Polarization
- Atomic Collisions
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- See eg
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- CALCULATIONS
- CHOOSE INITIAL CONDITIONS
- require Δzspin ~ 1mm use Bo = 10T a = 1 cm (iexcl105A) rarr vz ~ 105 ms (30 meV) rarr t ~ 10μs rarr Δxi ~ 100 μm
- Slide 25
- Slide 26
- Landau States
- Slide 28
- Slide 29
- Slide 30
- Fully quantum-mechanical calculation
- Slide 32
- Slide 33
- Slide 34
- Gedanken apparatus
- Slide 36
- Slide 37
- Conclusions
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Feasibility
-
Δz Δt = Δzv
Δv
v
B
δ δ δ
bull Gradient = B δ Gradient force = plusmn(μBB δ) acceldecel = plusmn(μBB meδ) = plusmn a
bull If 2aδ ltlt v2 time lag = Δt = 2aδv3
bull Let B = 1T δ = 01m Ebeam = 100 keV (β = 055) rarr Δt = 4 x 10-19 s ()
bull Since the transit time threough the magnet = 2 ns R ~ 10-8
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
- The Stern-Gerlach Effect for Electrons
- Electron Polarization
- Atomic Collisions
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- See eg
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- CALCULATIONS
- CHOOSE INITIAL CONDITIONS
- require Δzspin ~ 1mm use Bo = 10T a = 1 cm (iexcl105A) rarr vz ~ 105 ms (30 meV) rarr t ~ 10μs rarr Δxi ~ 100 μm
- Slide 25
- Slide 26
- Landau States
- Slide 28
- Slide 29
- Slide 30
- Fully quantum-mechanical calculation
- Slide 32
- Slide 33
- Slide 34
- Gedanken apparatus
- Slide 36
- Slide 37
- Conclusions
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Feasibility
-
Conclusions
bull The Bohr-Pauli analysis of Brillouinrsquos proposal is wrong
bull More generally their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails
bull A proper semi-classical analysis of Brillouinrsquos gedanken experiment yields Rayleigh-resolved spin states
bull A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and in principle arbitrarily large separation of spin states
bull Experiments to observe such spin-spitting are feasible (ie not totally insane) but would be very difficult
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
- The Stern-Gerlach Effect for Electrons
- Electron Polarization
- Atomic Collisions
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- See eg
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- CALCULATIONS
- CHOOSE INITIAL CONDITIONS
- require Δzspin ~ 1mm use Bo = 10T a = 1 cm (iexcl105A) rarr vz ~ 105 ms (30 meV) rarr t ~ 10μs rarr Δxi ~ 100 μm
- Slide 25
- Slide 26
- Landau States
- Slide 28
- Slide 29
- Slide 30
- Fully quantum-mechanical calculation
- Slide 32
- Slide 33
- Slide 34
- Gedanken apparatus
- Slide 36
- Slide 37
- Conclusions
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Feasibility
-
y
z
Hz
Hx
vz
xe-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
- The Stern-Gerlach Effect for Electrons
- Electron Polarization
- Atomic Collisions
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- See eg
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- CALCULATIONS
- CHOOSE INITIAL CONDITIONS
- require Δzspin ~ 1mm use Bo = 10T a = 1 cm (iexcl105A) rarr vz ~ 105 ms (30 meV) rarr t ~ 10μs rarr Δxi ~ 100 μm
- Slide 25
- Slide 26
- Landau States
- Slide 28
- Slide 29
- Slide 30
- Fully quantum-mechanical calculation
- Slide 32
- Slide 33
- Slide 34
- Gedanken apparatus
- Slide 36
- Slide 37
- Conclusions
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Feasibility
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
- The Stern-Gerlach Effect for Electrons
- Electron Polarization
- Atomic Collisions
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- See eg
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- CALCULATIONS
- CHOOSE INITIAL CONDITIONS
- require Δzspin ~ 1mm use Bo = 10T a = 1 cm (iexcl105A) rarr vz ~ 105 ms (30 meV) rarr t ~ 10μs rarr Δxi ~ 100 μm
- Slide 25
- Slide 26
- Landau States
- Slide 28
- Slide 29
- Slide 30
- Fully quantum-mechanical calculation
- Slide 32
- Slide 33
- Slide 34
- Gedanken apparatus
- Slide 36
- Slide 37
- Conclusions
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Feasibility
-
-0002
0002
b
-01
01x
(mm
)
a
0999 1000z (m)0
50
09997 10003z (m)0
50
num
ber
of e
-
Feasibility
- The Stern-Gerlach Effect for Electrons
- Electron Polarization
- Atomic Collisions
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- See eg
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- CALCULATIONS
- CHOOSE INITIAL CONDITIONS
- require Δzspin ~ 1mm use Bo = 10T a = 1 cm (iexcl105A) rarr vz ~ 105 ms (30 meV) rarr t ~ 10μs rarr Δxi ~ 100 μm
- Slide 25
- Slide 26
- Landau States
- Slide 28
- Slide 29
- Slide 30
- Fully quantum-mechanical calculation
- Slide 32
- Slide 33
- Slide 34
- Gedanken apparatus
- Slide 36
- Slide 37
- Conclusions
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Feasibility
-
Feasibility
- The Stern-Gerlach Effect for Electrons
- Electron Polarization
- Atomic Collisions
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- See eg
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- CALCULATIONS
- CHOOSE INITIAL CONDITIONS
- require Δzspin ~ 1mm use Bo = 10T a = 1 cm (iexcl105A) rarr vz ~ 105 ms (30 meV) rarr t ~ 10μs rarr Δxi ~ 100 μm
- Slide 25
- Slide 26
- Landau States
- Slide 28
- Slide 29
- Slide 30
- Fully quantum-mechanical calculation
- Slide 32
- Slide 33
- Slide 34
- Gedanken apparatus
- Slide 36
- Slide 37
- Conclusions
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Feasibility
-