COVID-19 Update: We are currently shipping orders daily. However, due to transit disruptions in some geographies, deliveries may be delayed. To provide all customers with timely access to content, we are offering 50% off Science and Technology Print & eBook bundle options. Terms & conditions.
Object-Oriented Magnetic Resonance - 1st Edition - ISBN: 9780080512976

Object-Oriented Magnetic Resonance

1st Edition

Classes and Objects, Calculations and Computations

Authors: Michael Mehring Volker Weberruss
eBook ISBN: 9780080512976
Imprint: Academic Press
Published Date: 12th June 2001
Page Count: 555
Sales tax will be calculated at check-out Price includes VAT/GST
Price includes VAT/GST

Institutional Subscription

Secure Checkout

Personal information is secured with SSL technology.

Free Shipping

Free global shipping
No minimum order.


This book presents, for the first time, a unified treatment of the quantum mechanisms of magnetic resonance, including both nuclear magnetic resonance (NMR) and electron spin resonance (ESR). Magnetic resonance is perhaps the most advanced type of spectroscopy and it is applied in biology, chemistry, physics, material science, and medicine. If applied in conjunction with spectroscopy, the imaging version of magnetic resonance has no counterpart in any type of experimental technique.

The authors present explanations and applications from fundamental to advanced levels.

Key Features

  • The authors present explanations and applications from fundamental to advanced levels
  • This groundbreaking volume is accompanied by software which simulates magnetic resonance phenomena


Students and scientists working with spectroscopy and imaging in physics, chemistry, material science, and medicine in academia and industry.

Table of Contents

Table of Contents



List of Graphical Symbols

1 Motivation

Spin Physics

2 A Quick Tour

2.1 Classes and Objects in Hilbert Space

2.1.1 The Class of Hilbert States

2.1.2 The Class of Spin Operators

2.1.3 The Class of Propagators

2.2 Classes and Objects in Liouville Space

2.2.1 The Class of Liouville States

2.2.2 The Class of Spin Superoperators

2.2.3 The Class of Superpropagators

3 The Objects in Hilbert Space

3.1 The Discrete Hilbert Space of Spin States

3.1.1 Zeeman States

3.1.2 Hilbert State Vectors

3.2 Operators I: Operators and Representations

3.2.1 The Two-Level System

3.2.2 The Three-Level System

3.2.3 The Multi-Level System

3.3 Operators II: Sets of Independent Operators

3.3.1 The Two-Level System

3.3.2 The Three-Level System

3.3.3 The Multi-Level System

3.4 Operators III: Rotations of Operators

3.4.1 Spin Operator Rotations

3.4.2 Tensor Operator Rotations

3.5 Operators IV: Density Operator and Density Matrix

3.5.1 Ensembles of Spin-1/2 Particles

3.5.2 Ensembles of Spin-I Particles

3.6 Operators V: Basis Changes

3.6.1 The Two-Level System

3.6.2 The Multi-Level System

3.7 Operators VI: Spin Hamiltonians

3.7.1 The Zeeman Hamiltonian

3.7.2 The Quadrupole Hamiltonian

3.8 Operators VII: Composite Spin Systems

3.8.1 Spin Operators of Two Spins I = 1/2

3.8.2 The Tensor Operators of Two Spins I = 1/2

3.8.3 The Density Operator of Two Spins I = 1/2

3.8.4 Interaction Hamiltonians of Two Spins I= 1/2

4 The Dynamics in Hubert Space

4.1 The Time Evolution

4.1.1 Object Dynamics in the Schrödinger Representation

4.1.2 Object Dynamics in the Heisenberg Representation

4.1.3 Object Dynamics in the Interaction Representation

4.2 The State Representation

4.2.1 Time-Independent Perturbation Expansion

4.2.2 Time-Dependent Perturbation Expansion

4.2.3 Product Representation

4.2.4 Magnus Expansion

4.3 Periodic Hamiltonians

4.3.1 Linearly and Circularly Polarized Excitations

4.3.2 An Introduction to the Average Hamiltonian Approach (AHA)

4.3.3 An Introduction to the Secular Averaging Approach (SAA)

4.4 Periodic Excitations

4.4.1 Fundamental Circularly Polarized Excitations

4.4.2 Linearly Polarized Excitations

5 The Objects in Liouville Space

5.1 The Liouville Space

5.1.1 Liouville States and Liouville Basis

5.1.2 Orthogonality and Completeness

5.1.3 Expectation Values

5.2 Liouville Operators I: Superoperators

5.2.1 Definition

5.2.2 Matrix Elements

5.2.3 Rotation Operations

5.3 Liouville Operators II: Composite Spin Systems

5.3.1 The Two-Spin Density Operator: Basis Operators

5.3.2 The Two-Spin Density Operator: Time Evolution

5.3.3 The Liouville Matrix

6 The Way to Magnetic Resonance

6.1 Classes, Objects, and Functions

6.1.1 Objects and Functions in Hubert Space

6.1.2 Objects and Functions in Liouville Space

6.2 Pulse Sequences

6.2.1 Pulse Sequence Operators

6.2.2 The Delta Pulse Approximation

6.2.3 The Density Matrix Before the First Pulse

6.3 Pulse Response Functions

6.3.1 Magnetic Resonance Response Functions

6.3.2 Fourier and Laplace Transformations

Magnetic Resonance

7 Spin Interactions and Spectra

7.1 Hamiltonians

7.1.1 External Interactions

7.1.2 Internal Interactions (NMR)

7.1.3 Internal Interactions (ESR)

7.2 Spectra

7.2.1 Shift Interaction Spectra

7.2.2 Quadrupolar Spectra

7.2.3 Spin-Spin Interaction Spectra

7.3 Rotations

7.3.1 Sample Rotation

7.3.2 Sample Spinning

7.3.3 Molecular Reorientation

8 Relaxation and Decoherence

8.1 Principles of Relaxation Measurements

8.1.1 The Spin-Lattice Relaxation

8.1.2 Spin-Spin Relaxation

8.1.3 Spin-Locking

8.2 Relaxation in the Rapid Motion Limit

8.2.1 Relaxation Rate and Memory Function

8.2.2 Fluctuating Local Fields

8.2.3 Relaxation Rates for Special Spin Interactions

8.2.4 Spin Fluctuations

8.3 Relaxation in the Slow Motion Limit

8.3.1 Relaxation and Memory Effects

8.3.2 Rapid Motion Limit

8.4 Models of Molecular Motion

8.4.1 Isotropie Molecular Reorientations

8.4.2 Anisotropie Molecular Reorientations

8.4.3 Discrete Jump Models

9 Spin Echos

9.1 The Hahn Echo in Inhomogeneous Fields

9.1.1 The Pulse Sequence of the Hahn Echo

9.1.2 The Response Function of the Hahn Echo

9.1.3 The Generalized Spin Echo Response Function

9.1.4 Phase Cycling

9.2 The Rotary Echo

9.2.1 The Pulse Sequence of the Rotary Echo

9.2.2 The Response Function of the Rotary FID

9.2.3 The Response Function of the Rotary Echo

9.3 The Driven Echo

9.3.1 The Pulse Sequence of the Driven Echo

9.3.2 The Response Function of the Driven Echo

9.4 The Stimulated Echo

9.4.1 Pulse Sequence and Response Function

9.4.2 The Genuine Stimulated Echo

9.5 The Quadrupolar Echo

9.5.1 The Pulse Sequence of the Quadrupolar Echo

9.5.2 The Response Function of the Quadrupolar Echo

9.5.3 The Primary Quadrupole Echo

9.5.4 Separation of Magnetic and Quadrupole Echos

9.5.5 Multiple Quadrupole Echos

9.6 The Solid Echo

9.6.1 The Pulse Sequence of the Solid Echo

9.6.2 The Response Function of the Solid Echo

9.7 The Magic Echo

9.7.1 The Magic Echo Pulse Sequence

9.7.2 The Magic Echo Condition

9.7.3 The Magic Sandwich Superpropagator

9.8 Echo Envelope Modulation

9.8.1 The Envelope Function of the Two-Pulse Echo

9.8.2 The Envelope Function of the Stimulated Echo

10 Double Resonance

10.1 Double Resonance in Three-Level Spin Systems

10.1.1 The Boltzmann Equilibrium

0.1.4 Spin Alignment

10.2 Double Resonance in Multi-Level Spin Systems

10.2.1 The «-Level Population

10.2.2 The z Magnetization

10.2.3 The Inverse Spin Temperatures

10.3 Electron Nuclear Double Resonance (ENDOR)

10.3.1 Population and Polarization Dynamics

10.3.2 Dynamic Nuclear Spin Polarization (DNP)

10.4 Spin Echo Double Resonance (SEDOR)

10.4.1 The Spin Echo Response Function without / Pulse

10.4.2 The Spin Echo Response Function with / Pulse

10.4.3 The Spin Echo Response Function with Time Variation

10.5 Proton Enhanced Nuclear Induction Spectroscopy

10.5.1 Cross Polarization (CP)

10.5.2 Adiabatic Demagnetization and Cross Polarization

10.5.3 Cross Polarization Dynamics

10.5.4 Spin Decoupling Dynamics

10.6 Pulsed ENDOR

10.6.1 Davies and TRIPLE ENDOR

10.6.2 Mims ENDOR

11 Multiple-Pulse Experiments

11.1 What are Multiple-Pulse Experiments?

11.2 Carr-Purcell-Meiboom-Gill Multiple-Spin Echo Train

11.2.1 The Carr-Purcell Pulse Sequence

11.2.2 The Meiboom-Gill Pulse Sequence

11.3 Chemical Shift Concertina

11.3.1 The Chemical Shift Concertina Pulse Sequence

11.3.2 Application of the Average Hamiltonian Theory

11.4 The WAHUHA Four-Pulse Experiment

11.4.1 The WAHUHA Pulse Sequence

11.4.2 Application of the Average Hamiltonian Theory

11.4.3 High-Resolution Solid State Spectra

11.5 The Flip-Flop Lee-Goldburg (FFLG) Experiment

11.5.1 The Lee-Goldburg (LG) Pulse Sequence

11.5.2 The Flip-Flop Lee-Goldburg (FFLG) Pulse Sequence

11.6 Advanced Multiple-Pulse Experiments

11.6.1 Eight-Pulse Cycles (HW-8 and MREV-8)

11.6.2 24-Pulse and 52-Pulse Cycles (BR-24 and BR-52)

11.6.3 Time Reversal Multiple-Pulse Cycles

12 Multiple-Quantum Spectroscopy

12.1 Multiple-Quantum Transitions

12.1.1 Multiple-Quantum Transitions in Multi-Spin Systems

12.1.2 Excitations by Strong Irradiation

12.1.3 Double-Quantum Decoupling

12.2 Time Domain Multiple-Quantum Spectroscopy

12.2.1 Multiple-Quantum Excitation, Evolution, and Detection

12.2.2 Multiple-Quantum Spectra

12.2.3 Time Reversal Sequences

12.2.4 Generalized Multiple-Quantum Theory

12.2.5 Selective MQ Pumping

12.3 Multiple-Quantum and Transient Sublevel ENDOR

12.3.1 Preparation for Sublevel ENDOR

12.3.2 Multiple-Quantum ENDOR

12.3.3 Transient Sublevel ENDOR

13 Two-Dimensional Spectroscopy

13.1 What is Two-Dimensional Spectroscopy?

13.2 Principles of 2D Fourier Spectroscopy

13.2.1 Magnetic Resonance Line Shapes in 2D Spectroscopy

13.2.2 Quantum Evolution in 2D Spectroscopy

13.2.3 Skewed and Sheared 2D Spectra

13.3 Separation of Interactions

13.3.1 Spin-Spin versus Shift Interactions

13.3.2 Correlation Spectroscopy (COSY)

13.3.3 Exchange Spectroscopy

13.4 Hyperfine Correlation Spectroscopy (HYSCORE)

13.4.1 The HYSCORE Response Function

13.4.2 The Case of S = 1/2 and I= 1/2

13.4.3 The Case of S = 1/2 and I=1

14 Spin Quantum Computing

14.1 First Steps in Quantum Computing

14.1.1 The NOT Gate

14.1.2 The CNOT Gate

14.1.3 The Toffoli Gate

14.1.4 The Quantum Bit

14.1.5 The Quantum Measurement

14.2 Elementary Spin Quantum Gates

14.2.1 The Spin Implementation of the NOT Gate

14.2.2 The Spin Implementation of the ?NOT Gate

14.2.3 The Spin Implementation of the CNOT Gate

14.2.4 The Spin Implementation of the SWAP Gate

14.2.5 The Spin Implementation of the Alternative Toffoli Gate

14.2.6 The NMR Implementation by Cory et al

14.2.7 The 2D NMR Representation of Quantum Gates

14.3 Entangled Spin States

14.3.1 Two-Qubit Systems

14.3.2 Three-Qubit Systems

14.3.3 Two-Bit Entangled State by CNOT Operation

14.4 Pseudo Pure and Mixed States

14.4.1 Mixed States

14.4.2 Pseudo Pure States

14.5 The Implementation of the Deutsch Algorithm

14.5.1 The Deutsch Algorithm

14.5.2 The NMR Implementation

14.6 The Implementation of the Grover Search Algorithm

14.6.1 The Grover Search Algorithm

14.6.2 The NMR Implementation

14.7 Quantum Error Correction and Teleportation

Complementary Analytical and Numerical Methods

15 Analytical Methods

15.1 The Floquet Approach (FA)

15.1.1 The Floquet Theorem

15.1.2 The Floquet Strategy

15.2 The Perturbation-Theoretical Approach (PTA)

15.2.1 The Evolution Operator

15.2.2 The Density Operator

15.2.3 The Operator Modes

15.2.4 The Decomposition Process

15.3 The Secular Averaging Approach (SAA)

15.3.1 The Evolution Operator

15.3.2 The Decomposition Process

15.4 Application: Linearly Polarized Excitations

15.4.1 The Total Evolution Operator in a Two-Level Spin System

15.4.2 The Total Density Operator in a Two-Level Spin System

15.4.3 The Magnetization Vector in a Two-Level Spin System

15.4.4 A Numerical Analysis

15.4.5 Remarks on the SAA

15.4.6 Remarks on the FA

15.5 FA, PTA, or SAA?


16.1 Installation

16.2 Programming Structures

16.3 Classes, Objects, and Functions



17 Lists

17.1 Objects

17.1.1 Tensor Operators

17.1.2 Hamiltonians

17.2 Object Transformation

17.2.1 Rotations of Tensor Operators

17.2.2 Rotations of Hamiltonians

17.3 Object Commutation



About the Authors


No. of pages:
© Academic Press 2012
12th June 2001
Academic Press
eBook ISBN:

About the Authors

Michael Mehring

Michael Mehring is the director of the Physikalische Institut at the Universität Stuttgart, Germany.

Affiliations and Expertise

Universitat Stuttgart, Germany

Volker Weberruss

Volker Achim Weberruß is a freelance physicist, producer of scientific book software, and the author of several scientific books.

Affiliations and Expertise

VAW Scientific Consultation, Winterbach, Germany

Ratings and Reviews