Object-Oriented Magnetic Resonance

Object-Oriented Magnetic Resonance

Classes and Objects, Calculations and Computations

1st Edition - June 12, 2001

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  • Authors: Michael Mehring, Volker Weberruss
  • eBook ISBN: 9780080512976

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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 GAMMA

    16.1 Installation

    16.2 Programming Structures

    16.3 Classes, Objects, and Functions

    16.4 GNUPLOT


    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

Product details

  • No. of pages: 555
  • Language: English
  • Copyright: © Academic Press 2012
  • Published: June 12, 2001
  • Imprint: Academic Press
  • eBook ISBN: 9780080512976

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

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