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