Nonrelativistic Quantum X-Ray Physics

Providing a solid theoretical background in photon-matter interaction, Nonrelativistic Quantum X-Ray Physics enables readers to understand experiments performed at XFEL-facilities and x-ray synchrotrons. As a result, after reading this book, scientists and students will be able to outline and perform calculations of some important x-ray-matter interaction processes. Key features of the contents are that the scope reaches beyond the dipole approximation when necessary and that it includes short-pulse interactions. To aid the reader in this transition, some relevant examples are discussed in detail, while non-relativistic quantum electrodynamics help readers to obtain an in-depth understanding of the formalisms and processes. The text presupposes a basic (undergraduate-level) understanding of mechanics, electrodynamics, and quantum mechanics. However, more specialized concepts in these fields are introduced and the reader is directed to appropriate references. While primarily benefiting users of x-ray light-sources, the material is equally of relevance to researchers in various disciplines, such as life sciences, biology, materials science, physics, and chemistry that plan on applying these new facilities in their respective fields.

Auteur
Stefan Hau-Riege is the X-ray Science and Technology Group Leader at the Lawrence Livermore National Laboratory (LLNL), where he works on x-ray free-electron-laser interactions with materials, x-ray instrumentation, and ultrafast imaging, drawing on computational and experimental physics. Previously, he worked on extreme-ultraviolet lithography and laser-assisted recrystallization. Dr. Hau-Riege received his Ph.D. in materials science from the MIT in 2000, and a M.S. in solid-state physics and applied mathematics from the University of Hamburg, Germany. He has authored and co-authored more than 100 scientific journal publications, and is co-inventor of more than 20 patents.

Contenu

Preface XIII

Part I Introduction 1

1 Introduction 3

1.1 Motivation 3

1.2 Comparing X-Rays with Optical Radiation 3

1.3 Novel X-Ray Sources 5

1.4 Unit Systems 6

1.5 Overview of Lagrangian and Hamiltonian Mechanics 9

1.5.1 Lagrangian Mechanics 9

1.5.2 Hamiltonian Mechanics 10

1.6 Approximations 12

1.6.1 Semiclassical Approximation 12

1.6.2 Dipole Approximation 13

2 Review of Some Concepts in Quantum Mechanics 15

2.1 Introduction 15

2.2 Dirac's BraKet (Bracket) Notation 15

2.3 Eigenvalues and Eigenfunctions 16

2.4 Functions of Operators 18

2.5 Point Particle in a Radially Symmetric Potential 19

2.5.1 Radial Schrödinger Equation 19

2.5.2 Bound States in a Modified Attractive Coulomb Potential 21

2.5.3 Unbound States in a Coulomb Potential 21

2.5.4 Pure Coulomb Potential 22

2.6 Mixed States 23

2.6.1 Isolated Systems 23

2.6.2 Coupled Systems 25

2.7 Schrödinger and Heisenberg Pictures of Quantum Mechanics 26

2.7.1 Evolution Operator in the Schrödinger Picture 26

2.7.2 Equivalent Pictures of Quantum Mechanics 28

2.7.3 Schrödinger Picture 28

2.7.4 Heisenberg Picture 29

2.8 Representing Quantum Mechanics in Position and Momentum Space 29

2.9 Transition from Classical Mechanics to Quantum Mechanics 31

2.10 Molecular Orbital Approximation 31

2.10.1 Derivation of the HartreeFock Equations 32

2.10.2 Interpretation of Orbital Energies 38

2.10.3 Post-HartreeFock Methods 40

Part II Quantization of the Free Electromagnetic Field 41

3 Classical Electromagnetic Fields 43

3.1 Introduction 43

3.2 Maxwell's Equations 43

3.3 Electromagnetic Potentials 44

3.3.1 Field Equations 44

3.3.2 Gauge Transformation 45

3.3.3 Coulomb Gauge 45

3.3.4 Lorenz Gauge 46

3.4 Transverse and Longitudinal Maxwell's Equations 46

3.4.1 Helmholtz Decomposition of Maxwell's Equations 47

3.4.2 Decomposition of the Field Equations in the Coulomb Gauge 47

3.5 The Free Electromagnetic Field as a Sum of Mode Oscillators 48

3.5.1 Density of States of the Radiation Field 53

3.5.2 Radiation Cavity in Thermodynamic Equilibrium 54

3.6 Charged Particle in an Electromagnetic Field and the Minimal-Coupling Hamiltonian 56

4 Harmonic Oscillator 59

4.1 Introduction 59

4.2 Classical Harmonic Oscillator with One Degree of Freedom 59

4.3 Quantum Mechanical Harmonic Oscillator 60

4.4 N-Dimensional Quantum Mechanical Harmonic Oscillator 64

5 Quantization of the Electromagnetic Field 67

5.1 Introduction 67

5.2 Transition to a Quantum Mechanical Description 67

5.3 Photon Number States (Fock States) 71

5.4 Photons 73

5.4.1 Photon Momentum and Poynting Vector 73

6 Continuous Fock Space 77

6.1 Introduction 77

6.2 Three-Dimensional Continuum Field 77

6.2.1 Number States in the Continuum Field 80

6.3 One-Dimensional Treatment 84

6.3.1 Intensity 85

6.3.2 Description in the Time Domain 86

7 Coherence 89

7.1 Introduction 89

7.2 Review of Classical Coherence Theory 89

7.2.1 First-Order Coherence 90

7.2.2 Second-Order Coherence 92

7.2.3 Chaotic Light 93

7.3 Quantum Coherence Theory 96

7.3.1 Coincidence Detection Using an Ideal Photon Detector 96

7.3.2 Field Correlations 98

7.3.3 Coherence 101

8 Examples for Electromagnetic States 103

8.1 Introduction 103

8.2 Quantum Phase of Radiation Fields 103 8.2.1 Dirac's Phase Operato...