Nonrelativistic Quantum X-Ray Physics -- Contents -- Preface -- Part I Introduction -- Chapter 1 Introduction -- 1.1 Motivation -- 1.2 Comparing X-Rays with Optical Radiation -- 1.3 Novel X-Ray Sources -- 1.4 Unit Systems -- 1.5 Overview of Lagrangian and Hamiltonian Mechanics -- 1.5.1 Lagrangian Mechanics -- 1.5.2 Hamiltonian Mechanics -- 1.6 Approximations -- 1.6.1 Semiclassical Approximation -- 1.6.2 Dipole Approximation -- Chapter 2 Review of Some Concepts in Quantum Mechanics -- 2.1 Introduction -- 2.2 Dirac's Bra-Ket (Bracket) Notation -- 2.3 Eigenvalues and Eigenfunctions -- 2.4 Functions of Operators -- 2.5 Point Particle in a Radially Symmetric Potential -- 2.5.1 Radial Schrödinger Equation -- 2.5.2 Bound States in a Modified Attractive Coulomb Potential -- 2.5.3 Unbound States in a Coulomb Potential -- 2.5.4 Pure Coulomb Potential -- 2.6 Mixed States -- 2.6.1 Isolated Systems -- 2.6.2 Coupled Systems -- 2.7 Schrödinger and Heisenberg Pictures of Quantum Mechanics -- 2.7.1 Evolution Operator in the Schrödinger Picture -- 2.7.1.1 Evolution of Pure States -- 2.7.1.2 Evolution of Mixed States -- 2.7.2 Equivalent Pictures of Quantum Mechanics -- 2.7.3 Schrödinger Picture -- 2.7.4 Heisenberg Picture -- 2.8 Representing Quantum Mechanics in Position and Momentum Space -- 2.9 Transition from Classical Mechanics to Quantum Mechanics -- 2.10 Molecular Orbital Approximation -- 2.10.1 Derivation of the Hartree-Fock Equations -- 2.10.1.1 Energy of the Slater Determinant -- 2.10.1.2 Energy Minimization of the Slater Determinant -- 2.10.2 Interpretation of Orbital Energies -- 2.10.2.1 Ionization Potential -- 2.10.2.2 Electron Affinity -- 2.10.3 Post-Hartree-Fock Methods -- PartII Quantization of the Free Electromagnetic Field -- Chapter 3 Classical Electromagnetic Fields -- 3.1 Introduction -- 3.2 Maxwell's Equations.

3.3 Electromagnetic Potentials -- 3.3.1 Field Equations -- 3.3.2 Gauge Transformation -- 3.3.3 Coulomb Gauge -- 3.3.4 Lorenz Gauge -- 3.4 Transverse and Longitudinal Maxwell's Equations -- 3.4.1 Helmholtz Decomposition of Maxwell's Equations -- 3.4.2 Decomposition of the Field Equations in the Coulomb Gauge -- 3.5 The Free Electromagnetic Field as a Sum of Mode Oscillators -- 3.5.1 Density of States of the Radiation Field -- 3.5.2 Radiation Cavity in Thermodynamic Equilibrium -- 3.5.2.1 Rayleigh - Jeans Radiation Law -- 3.5.2.2 Planck's Radiation Law -- 3.6 Charged Particle in an Electromagnetic Field and the Minimal-Coupling Hamiltonian -- Chapter 4 Harmonic Oscillator -- 4.1 Introduction -- 4.2 Classical Harmonic Oscillator with One Degree of Freedom -- 4.3 Quantum Mechanical Harmonic Oscillator -- 4.4 N-Dimensional Quantum Mechanical Harmonic Oscillator -- Chapter 5 Quantization of the Electromagnetic Field -- 5.1 Introduction -- 5.2 Transition to a Quantum Mechanical Description -- 5.3 Photon Number States (Fock States) -- 5.4 Photons -- 5.4.1 Photon Momentum and Poynting Vector -- Chapter 6 Continuous Fock Space -- 6.1 Introduction -- 6.2 Three-Dimensional Continuum Field -- 6.2.1 Number States in the Continuum Field -- 6.2.1.1 Vacuum State -- 6.2.1.2 One-Photon States -- 6.2.1.3 Single-Mode Multiple-Photon States -- 6.2.1.4 Multimode States -- 6.3 One-Dimensional Treatment -- 6.3.1 Intensity -- 6.3.2 Description in the Time Domain -- Chapter 7 Coherence -- 7.1 Introdcution -- 7.2 Review of Classical Coherence Theory -- 7.2.1 First-Order Coherence -- 7.2.2 Second-Order Coherence -- 7.2.3 Chaotic Light -- 7.2.3.1 First-Order Coherence of SASE FELs -- 7.2.3.2 Second-Order Coherence of SASE FELs -- 7.3 Quantum Coherence Theory.

7.3.1 Coincidence Detection Using an Ideal Photon Detector -- 7.3.2 Field Correlations -- 7.3.3 Coherence -- Chapter 8 Examples for Electromagnetic States -- 8.1 Introduction -- 8.2 Quantum Phase of Radiation Fields -- 8.2.1 Dirac's Phase Operator -- 8.2.2 Quantum Sine and Cosine Operators -- 8.2.3 Phase State Projectors -- 8.3 Single-Mode States -- 8.3.1 Pure Single-Mode States -- 8.3.2 Statistical Mixtures of Single-Mode States -- 8.3.2.1 Thermally Excited States -- 8.3.3 Coherent States -- 8.4 Multimode States -- 8.4.1 Multimode Fock States -- 8.4.2 Multimode Coherent States -- 8.4.3 Localized Radiation (Wave Packets Describing Localized Photons) -- 8.4.3.1 Gaussian Wave Packets -- 8.4.4 Chaotic Light -- 8.4.4.1 Thermally Excited Multimode States -- 8.5 One-Dimensional Continuum Mode States -- PartIII Interaction of X-Rays with Matter -- Chapter 9 Interaction of the Electromagnetic Field with Matter -- 9.1 Introdution -- 9.2 Tensor Product of Matter and Radiation Hilbert Spaces -- 9.3 Interaction Hamiltonian for the Electromagnetic Field and Matter -- Chapter 10 Time-Dependent Perturbation Theory -- 10.1 Introduction -- 10.2 Interaction Picture -- 10.2.1 Pure States -- 10.2.2 Mixed States -- 10.3 Transition Probabilities -- 10.3.1 Time Dependence of Perturbations -- 10.3.2 Transition Probabilities -- 10.3.2.1 Pure States -- 10.3.2.2 Mixed States -- 10.4 Perturbative Expansion of Transition Amplitudes -- 10.4.1 Transition Amplitude in First Order -- 10.4.2 Transition Amplitude in Second Order -- 10.4.3 Transition Between Discrete States -- 10.4.4 Transition from Discrete to Continuous States -- 10.4.4.1 Example: Free Particle -- 10.4.5 Transition Between Continuous States -- 10.4.6 Scattering (Ŝ) and Transition (T) Matrices -- 10.5 Time-Dependent Perturbation Theory for Mixed States -- 10.5.1 Isolated System.

10.5.2 Coupled Systems -- Chapter 11 Application of Perturbation Theory to the Interaction of Electromagnetic Fields with Matter -- 11.1 Introduction -- 11.2 Feynman Diagrams -- 11.3 Mixed States -- 11.3.1 Transition Probabilities -- PartIV Applications of X-Ray-Matter-Interaction Theory -- Chapter 12 X-Ray Scattering by Free Electrons -- 12.1 Introduction -- 12.2 Energy and Momentum Conservation -- 12.2.1 Scattering of Photons by Free Electrons -- 12.2.2 A Free Electron Cannot Absorb a Photon -- 12.3 Scattering Cross Section -- 12.4 Scattering From an Electron at Rest -- 12.4.1 Kinematics -- 12.4.2 Nonrelativistic Scattering Cross Section -- 12.4.3 Polarization -- 12.4.4 Relativistic Klein-Nishima Cross Section -- 12.5 Doppler Effect -- Chapter 13 Radiative Atomic Bound - Bound Transitions -- 13.1 Introduction -- 13.2 Emission of Photons -- 13.3 Lifetime and Natural Line Width -- 13.3.1 Weisskopf - Wigner Theory -- 13.3.2 Frequency Spectrum -- 13.3.3 Breit - Wigner Procedure -- 13.4 Absorption of Photons -- 13.5 Einstein's A and B Coefficients -- 13.6 Radiative Atomic Bound - Bound Transitions in Mixed States -- Chapter 14 One-Photon Photoionization -- 14.1 Introduction -- 14.2 Photoionization in a Pure-State Radiation Field -- 14.3 Photoionization in a Mixed-State Radiation Field -- 14.4 Single-Electron Approximation for Photoionization -- 14.5 Photoionization of Hydrogen-Like Atoms -- 14.5.1 Large Photon Energies -- 14.5.2 Small Photon Energies -- 14.5.3 Comparing Small and Large Photon Energies -- Chapter 15 Bremsstrahlung -- 15.1 Introduction -- 15.2 Electron - Nucleus Bremsstrahlung -- 15.3 Electron - Positron Bremsstrahlung -- 15.4 Electron - Electron Bremsstrahlung -- 15.4.1 Quadrupole Nature of Bremsstrahlung -- 15.4.2 Indistinguishable Particles -- 15.5 Inverse Bremsstrahlung Absorption.

Chapter 16 X-Ray Scattering -- 16.1 Introduction -- 16.2 Steady-State Scattering Formalism -- 16.2.1 Dipole Approximation -- 16.3 Elastic Scattering (Rayleigh Scattering) -- 16.3.1 Elastic Scattering for Large X-Ray Energies -- 16.3.2 Elastic Scattering for Intermediate X-Ray Energies -- 16.4 Raman Scattering -- 16.5 Compton Scattering -- 16.5.1 Nonresonant Compton Scattering -- 16.5.2 Resonant Raman-Compton Scattering -- 16.5.3 Infrared Divergence for Soft Scattered Photon Energies -- 16.6 Single-Electron Approximation for X-Ray Scattering -- 16.7 Short-Pulse Scattering -- 16.7.1 General Formalism -- 16.7.2 Plane-Parallel Light Pulse -- 16.7.3 Coherent Pulses -- Chapter 17 Relaxation Processes -- 17.1 Introduction -- 17.2 Auger Decay -- 17.2.1 Eigenstates Due to Coupling of a Discrete Level to a Continuum -- 17.2.1.1 Decay Rate -- 17.2.2 Autoionization in First-Order Perturbation Theory -- 17.2.2.1 Wentzel Treatment of the Auger Effect -- 17.2.2.2 Estimate for the Auger Rates -- 17.3 X-Ray Fluorescence following Photoionization -- 17.4 Branching Ratio -- Chapter 18 Multiphoton Photoionization -- 18.1 Introduction -- 18.2 Above-Threshold Ionization -- 18.3 Sequential Two-Photon Absorption -- Chapter 19 Threshold Phenomena -- 19.1 Introduction -- 19.2 One-Step Treatment of Threshold Excitations -- 19.3 Nonradiative Threshold Processes -- 19.3.1 Shake-Modified Resonant Autoionization -- 19.3.2 Post-Collision Interaction -- References -- Index -- EULA.