Object-Oriented Magnetic Resonance

Table of ContentsPreface Notation 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.