every
reader
hydrogen spectrum.
energy
of
the
initial
state
E^
quantum
that
the
new
mechanics
quantum
mechanics
probabilities.
We
now
)(
).
is said
to be
...8-<).
the
representatives
of
the
individual
<|/s;
/(*)*&.
for the
have
all
the
properties
values
over
Xx(
wT
)>
experimental
operations
||(A
|r
shall return
set
of
magnitude
while
the
K
distance
eigenvalues.
for
that
of
10
2
the
roots
must
be
obtained
very
accurately
to
give
moderate
accuracy
in
the
transformation
coefficients
to
commute
when
this
dyadic
vanishes,
i.e.
\
vanishing
by
UITOBB
and
SHOETLEY,
Phys.
Rev.
42,
167
(1932).
of
these
T
which
satisfies
the
com
mutation
rule
^ T]
)
=
We
shall
later
wish
to
V0*+m+l)(j
1
or,
from
10
3
2a
Similarly,
from
(4),
or
have
adopted
(8)
Jim
-A
*
(*
?
the
association
of
j
a
and
jb
with
the
top
row,
however,
final
quantum
the
volume
element
dxdydz
KT i
A
to
have
poten
tials
are
computed.
state,
and
=-
terms
a
simple
linear
oscillator.
In
this
case,
in
any
direction
of
observation,
the
radiation
is
linearly
polarized
factor
times
the
identical
dyadic,
and
ZEMANSKY,
Resonance
Radiation
and
Excited
Atoms,
Cambridge
University
Press,
1934.
call
intensities.
Before
calculating
S(A,
B)
light
frequency
corresponds
to
a
transition
frequency
to
within
refraction,
that
is,
double
a
quantum
mechanically
that
it
is
always
Hermitian
(with
regard
that the
in
the
lowest
energy
propagation
If
we
are
dealing
with
band and
relativistic
origin
the
screening
of
the
orbital
electrons
momenta
in
order
that
the
operators
d/dx
be
on
an
value of
these states. If
discovered
(16)
prior
them
out
strengths
of
the
lines,
(a)
S(3
2
(see
Appendix).
differences of
the term
constants.
A
critical
study
=
s and
sharp
in
quantum
mechanics
as
all
of
the
eigenfunctions
have
non-vanishing
Intervals
14
Fig.
8
5
. Variation
z
-}-S
3
large
part
of
PJ/
5^^
or
j/$
vanish.
The
factor
1/VFI
is
placed
in
This was
6
6
are
identical
the
sum of the values
a
quantity.
Then
we
may
write
individual
sets
of
B
are
arranged
(2).
The
same
argument
applies
for
in A
(9)
i~
I
This
completes
non-vanishing
terms
which
(ab\q\cd)=-
m
^lmt).
(7)
If
we
now
introduce
the
abbreviation
^nW)
R
2
(nW)
dr^
(8)
quantum
numbers.
Consider
separately
the
4~A
It/ ( A,
shell. We do
consideration.
Therefore
they
do
not
affect
the
relative
positions
of
give
(1)
r
l
J
fi
In
other
with
of
the
new
states
the
terms
are
eliminated
by
i/S=
s
(l
(
}
plete
set.
The
interval
rule.
It
(1+0+)
)
=
OH
are
probably
theory predicts
an alternation:
are
great
enough
a
configuration
in
which
a
term
F&
coefficients
were
all
zero,
the
points
should
Ni IX
Observed
term
the
in a
p
2
illustrated
by
the
plot,
in
Fig.
I
8
rtanr
over
all
the
individual
S
M.L
scheme
may
be
obtained
by
the
nmltiplieation
(of.
proper
relative
phases
group.
The
product
of
these
two
states
will
be
a
known
linear
Q{
1,
-1+)
-$(1-
0+
the
definite
electron
 
terms
*F,
4
P
way
are
1^
1
parity.
been
observed,
and
that
L)\*, (4)
(5)
Thus
for
any
Eussell-Saunders
multiplet
we
have
derived
the
general
result
called the
a
given
L,
L
l
the value
strengths
of
4^3
}
)\*.
of this
by
Prokof
jew*
and
found
to
be
3
: 2
in
strengths
are
given
by
other
formulas
(3
17
intensity
data
are
merely
eye
estimates
from
plates
radial
integral
2
I*?
mf)
(cf.
4
5
M=l,
and since
two
states
with
Jfef
with
M
this
way
if
stringent
than
the
lT
J
JT)
angular
momentum
J
1
electrostatic
energy
is
completely
diagonal
{the
diagonal
elements
being
JJ/J
which
occurs
for
the
con
figuration
is
usually
electrons
are
equivalent.
).
-5
4
*S
-4
-3
2
x
S
L
J
equivalent
to
in
general
between these
k
3=
may
be
two
independent
^"-coupling
separately
calculated.
Configuration
3t
consists
of
a
closed
the closed
shell SP
-
with the
that
the
individual
configurations
do
not
in J
to
empirical
spectroscopists
(cf.
Fig.
6
7
*
tonian in
for
each
configuration;
a
break
in
the
wave-number
scale
indicates
the
separation
between
the
two
groups
of
levels.
The
scales
are
,
down
be
observed)
is
field
Z7(r).
Tor
such
a
field
the
energy
levels
are
given
by
5
5
1
1
including
the
relativity
and
spin
effects.
The
development
of
such
a
theory
of
the
X-ray
the
doublet
intervals
in
X-ray
spectra.
I
number
of
3d ,
the
departure
of
the
effective
field
from
the
hydrogen.
Looking
back
we
periods.
There
parentheses
for
treat
ment
of
the
first
long
period
differs
from
rather
4
odd*
series
of
the
long
period.
With
these
an
a
and
a
p
shell
are
being
filled,
so
we
expect
them
that
x
the
general
principles
of
Chapter
n
results
were,
in
Rydberg
units:
Li
II
He
I
Evidently
the
method
could
be
applied
a
charge
tion
problem
are
not
directly
comparable
as
they
stand,
since
they
the action
of the
f
follow
the
current
literature.
According
to
a
summary
prepared
by
Hartree
from
this
group
(and
from
others
also);
for
an
increase
of
Z
means
that
consequence
the
state
assumes
something
ofthe
character
of
continuum is
moves
in
an
orbit
which
extends
to
infinity.
Hence
as
a
result
of
interaction
with
intensity
calculate
the
relative
transition
probabilities
forthe
different
configuration
transitions
to
with
measurements
of
these
transition
probabilities.
5.
Spin-orbit
perturbation
toward
lower
frequency
from
the
unperturbed
line
by
the
transformation
coefficients
(y
SL
of course in an atom there are an infinite number
of levels
(rr}\
3
gauss,
Paschen
and
Back
publish
that
the
uncertainty
of
the
points
theory.
Voigt
gave
attention
to
I
k
2
is
transitions,
(c)
excitation
conditions
may
put
unequal
than the
at such
the electric
a
direct
discussion
of
equations
1
17
4
is
cautious
and
conservative,
Avoiding
the
leaky
barrier;
quantum
(6-4)
2
w
4
than
0-1
cm-
1
thousand
of 9
of
10
3
to
write
down
formulas
same
n
the
secular
equation
with
hydrogenic
matrix
components.
some
energy.
The
effect
of
this
on
the
atomic
energy
the
reduction
nuclei which
resultant
Fis
the
vector
sum
splitting
of
a
line
ending
on
the
Z
S
level,
by
Breit
and
Wills,*
while
the
importance
of
considering
the
1
is
of
the
manipulation
and
observation
by
a
human
observer.
To
recognize
deplore
it.
Certainly
the
egs
system
is
convenient
for
description
149,
169,
390
Kamijima,
415
Kassner,
400
Kayser,
3
Kellner,
346
Kelloscr,
421
Kent,
140,
153
et
seq.
Kimball,
44
Kirchner,
138
Kirschbaum,
401
Kiuti,
402,
403
Kopfermann,
107
Korff,
147
Kramers,
107,