Is Quantum Mechanics necessary for
understanding
Magnetic Resonance?
Is Quantum Mechanics necessary
for understanding
Magnetic Resonance?Magnetic Resonance?
Bita Samimizad
Magnetic Resonance?
Bita Samimizad
June 10th,2013
Based on a Paper by
Lars. G Hanson
1Magnetic Resonance and Quantum
Mechanics
OverviewOverview
Introduction
Misinterpretations
Magnetic Resonance and Quantum Mechanics2
Discussion
Conclusion
Introduction
� Transition from Classical Physics to Quantum Mechanics
Magnetic Resonance and Quantum Mechanics
Wolfgang Pauli and Niels Bohr look at
a spinning top. Bohr and Pauli are
pioneers of quantum mechanics,
where the concept of spin is rooted
Bohr–Einstein
debates
3
� Probabilistic Nature of Quantum Mechanics
� Understanding and Interpreting Quantum Mechanics
Phenomena
� Role of QM in Explaining MR
Magnetic Resonance and Quantum Mechanics
� Role of QM in Explaining MR
� MR and Correspondence Principle
Introduction4
Misinterpretations of Quantum Mechanics in MR and Misinterpretations of Quantum Mechanics in MR and
MythsMyths
� First Myth: According to QM, Protons align Either Parallel or
Antiparallel to the Magnetic field
� A Classical Analogy� A Classical Analogy
� Spin States and Uncertainty
Magnetic Resonance and Quantum Mechanics Myth 15
What is the Origin of Misconception?What is the Origin of Misconception?
� Magnetization of an Individual Proton
� Ensemble of Particles in a Magnetic Field
Magnetic Resonance and Quantum Mechanics Myth 16
Magnetic Resonance and Quantum Mechanics Myth 1
Comparing
Two
Illustrations
of Spin
Eigenstates
7
Analyzing the Problem for a two particle SystemAnalyzing the Problem for a two particle System
Polarization= +1 , 0 , -1
An MR measurement does not make the state of an Ensemble
collapse into single particle eigenstates
Magnetic Resonance and Quantum Mechanics Myth 1
Measurement of zero total Magnetization:
Entanglement of the states of two particles
8
� Second Myth: MR is a Quantum Effect
� How is a Quantum Effect defined?
� Some examples of Quantum Phenomena
� Bloch Vector and Two Quantum-Level Systems
Magnetic Resonance and Quantum Mechanics Myth 29
Quantum Mechanics and Classical Physics Give the Same Quantum Mechanics and Classical Physics Give the Same
PredictionsPredictions
�Density operator formalism as an alternative to vector approach
� Coherent evolution described by Liouville equation:
Magnetic Resonance and Quantum Mechanics Myth 2
� Coherent evolution described by Liouville equation:
� Density Operator and Coherency
10
X Component of Proton Magnetic Moment:
Expectation value of Magnetic Moment:
Magnetic Resonance and Quantum Mechanics Myth 2
Using Liouville Equation:
11
Having Dipole Hamiltonian as
We can write the equation above as:
Magnetic Resonance and Quantum Mechanics Myth 2
We can write the equation above as:
Which is exactly equivalent to the Classical Evolution.
12
dr/dt=ω×r
� Counter_Feynman approach in MR
� Zeeman Splitting and RF Field
Magnetic Resonance and Quantum Mechanics Myth 213
� Coherent Evolution as the Crucial point of
Understanding Magnetic Resonance
� Third Myth: RF Pulses Bring the Precessing Spin into Phase
Magnetic Resonance and Quantum Mechanics Myth 3
� RF field never changes the relative orientation between
noninteracting proton spins
� RF field never changes Coherence ( nonrandom phase relations)
� T1 as Real source of Coherence
14
Visualization of Spin Precession in Magnetic Fields Visualization of Spin Precession in Magnetic Fields
and and
Magnetic Resonance and Quantum Mechanics Myth215
Equilibrium Magnetization for Small Degrees of PolarizationEquilibrium Magnetization for Small Degrees of Polarization
Classical and QM PredictionsClassical and QM Predictions
Relative population expressed in diagonal elements of equilibrium Relative population expressed in diagonal elements of equilibrium
density operator:density operator:
Magnetic Resonance and Quantum Mechanics Myth 3
: Same expression with different sign of numerator exponent : Same expression with different sign of numerator exponent
The net magnetization per nucleus The net magnetization per nucleus
16
The approximation for small Degree of Polarization
Magnetic Resonance and Quantum Mechanics Myth 317
For small degrees of polarization we get the same result from
Classical Mechanics and QM.
Nature , Reality , our Perception Nature , Reality , our Perception
Different approachesDifferent approaches
� Mental Representation, Simplification of Reality
Magnetic Resonance and Quantum Mechanics Discussion
� Intuitiveness, simplicity and Prediction as Criteria
�Classical and Quantum Mechanics Approach of MR
18
ConclusionConclusion
� MR is not extremly complicated and QM ist not responsible
because MR is a classical phenomena.
� Basic NMR can be explained by QM but the interpretation is
Magnetic Resonance and Quantum Mechanics Conclusion
� Basic NMR can be explained by QM but the interpretation is
often problematic.
� A classical introduction to MR can provide intuition and
predictive power.
19
Thank you for your Attention
Magnetic Resonance and Quantum Mechanics The End
Thank you for your Attention
Sources:
Levitt MH. 2008. Spin Dynamics: Basics of Nuclear Magnetic
Resonance, 2nd ed. Chichester, England: Wiley.
David J. Griffiths Electrodynamics 1999
Nouredin Zettili Quantum Mechanics 2009
Hanson LG. 2007. Graphical simulator for teaching
basic and advanced MR imaging techniques. Radio-
Graphics 27:e27.
Magnetic Resonance and Quantum Mechanics Sources
Graphics 27:e27.
Feynman RP, Vernon FL, Jr., Hellwarth RW. 1957.
Geometrical representation of the Schrödinger equation
for solving MASER problems. J Appl Phys 28:
49–52.
J.J Sakurai,Modern Quantum Mechanics
Source of Images:
https://en.wikipedia.org/wiki/Magnetic_resonance_imaging
http://physicsworld.com/cws/article/news/2013/may/23/quantum-microscope-peers-
into-the-hydrogen-atom
http://allthatmatters.heber.org/2010/12/17/get-those-computers-spinning/
Magnetic Resonance and Quantum Mechanics sources
http://www.freewallpaperpic.com/wp/einstein/0800/Albert_Einstein_1925_Niels_Bo
hr_by_Paul_Ehrenfest.jpg
http://www.slideboom.com/presentations/323013
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