Preface 1 The Theory of Special Relativity 1.1 The Lorentz Transformations 1.2 Relativistic Velocities 1.3 Mass, Momentum and Energy 1.4 Four-Vectors 1.5 Relativity and Electromagnetism 1.6 The Compton Effect 1.7 Problems
2 Aspects of Angular Momentum 2.1 Various Angular Momenta 2.2 Angular Momentum and Rotations 2.3 Operators and Eigenvectors for Spin 1/2 2.4 Operators for Higher Spins 2.5 Orbital Magnetic Moments 2.6 Spin Without Relativity 2.7 Thomas Precession 2.8 The Pauli Equation in a Central Potential 2.9 Dirac Notation 2.10 Clebsch-Gordan and Racah Coefficients 2.11 Relativistic Quantum Numbers and Spin-Angular Functions 2.12 Energy Levels of the One-Electron Atom 2.13 Plane Wave Expansions 2.14 Problems
3 Particles of Spin Zero 3.1 The Klein-Gordon Equation 3.2 Relativistic Wavefunctions, Probabilities and Currents 3.3 The Fine Structure Constant 3.4 The Two-Component Klein-Gordon Equation 3.5 Free Klein-Gordon Particles/Antiparticles 3.6 The Klein Paradox 3.7 The Radial Klein-Gordon Equation 3.8 The Spinless Electron Atom 3.9 Problems
4 The Dirac Equation 4.1 The Origin of the Dirac Equation 4.2 The Dirac Matrices 4.3 Lorentz Invariance of the Dirac Equation 4.4 The Non-Relativistic Limit of the Dirac Equation 4.5 An Alternative Formulation of the Dirac Equation 4.6 Probabilities and Currents 4.7 Gordon Decomposition 4.8 Forces and Fields 4.9 Gauge Invariance and the Dirac Equation 4.10 Problems
5 Free PaNicles/Antiparticles 5.1 Wavefunctions, Densities and Currents 5.2 Free-Particle Solutions 5.3 Free-Particle Spin Rotations and Spinors A Generalized Spin Operator 5.4 Negative Energy States, Antiparticles 5.5 Classical Negative Energy Particles? 5.6 The Klein Paradox Revisited 5.7 Lorentz Transformation of the Free-Particle Wavefunction 5.8 Problems
6 Symmetries and Operators 6.1 Non-Relativistic Spin Projection Operators 6.2 Relativistic Energy and Spin Projection Operators 6.3 Charge Conjugation 6.4 "lime-Reversal Invariance 6.5 Parity 6.6 6.7 Angular Momentum Again 6.8 Non-Relativistic Limits Again 6.9 Second Quantization 6.10 Field Operators 6.11 Second Quantization in Relativistic Quantum Mechanics 6.12 Problems
7 Separating Particles from Antiparticles 7.1 The Foldy-Wouthuysen Transformation for a Free Particle 7.2 Foldy-Wouthuysen Transformation of Operators 7.3 Zitterbewegung 7.4 Foldy-Wouthuysen Transformation of the Wavefunction 7.5 The F-W Transformation in an Electromagnetic Field 7.6 Problems
8 One-Electron Atoms 8.1 The Radial Dirac Equation 8.2 Free-Electron Solutions 8.3 One-Electron Atoms, Eigenvectors and Eigenvalues 8.4 Behaviour of the Radial Functions 8.5 The Zeeman Effect 8.6 Magnetic Dichroism 8.7 Problems
9 Potential Problems 9.1 A Particle in a One-Dimensional Well 9.2 The Dirac Oscillator The Non-Relativistic Limit Solution of the Dirac Oscillator Expectation Values and the Uncertainty Principle 9.3 Bloch's Theorem 9.4 The Relativistic Kronig-Penney Model A One-Dimensional Time-Independent Dirac Equation A Potential Step A One-Dimensional Solid 9.5 An Electron in Crossed Electric and Magnetic Fields An Electron in a Constant Magnetic Field An Electron in a Field for which 9.6 Non-Linear Dirac Equations, the Dirac Soliton 9.7 Problems
10 More Than One Electron 10.1 The Breit Interaction 10.2 Two Electrons 10.3 Many-Electron Wavefunctions 10.4 The Many-Electron Hamiltonian 10.5 Dirac-Hartree-Fock Integrals Single-Particle Integrals Two-Particle Integrals The Direct Coulomb Integral The Exchange Integral 10.6 The Dirac-Hartree-Fock Equations The One-Electron Atom The Many-Electron Atom 10.7 Koopmans' Theorem 10.8 Implementation of the Dirac-Hartree-Fock Method 10.9 Introduction to Density Functional Theory 10.10 Non-Relativistic Density Functional Theory 10.11 The Variational Principle and the Kohn-Sham Equation 10.12 Density Functional Theory and Magnetism Density Functional Theory in a Weak Magnetic Field Density Functional Theory in a Strong Magnetic Field 10.13 The Exchange-Correlation Energy 10.14 Relativistic Density Functional Theory (RDFT) RDFT with an External Scalar Potential RDFT with an External Vector Potential The Dirac-Kohn-Sham Equation 10.15 An Approximate Relativistic Density Functional Theory 10.16 Further Development of RDFT 10.17 Relativistic Exchange-Correlation Functionals 10.18 Implementation of RDFT
11 Scattering Theory 11.1 Green's Functions 11.2 Time-Dependent Green's Functions 11.3 The T-Operator 11.4 The Relativistic Free-Particle Green's Function 11.5 The Scattered Particle Wavefunction 11.6 The Scattering Experiment 11.7 Single-Site Scattering in Zero Field 11.8 Radial Dirac Equation in a Magnetic Field 11.9 Single-Site Scattering in a Magnetic Field 11.10 The Single-Site Scattering Green's Function 11.11 Transforming Between Representations 11.12 The Scattering Path Operator 11.13 The Non-Relativistic Free Particle Green's Function 11.14 Multiple Scattering Theory 11.15 The Multiple Scattering Green's Function 11.16 The Average T-Matrix Approximation 11.17 The Calculation of Observables The Band Structure The Fermi Surface The Density of States The Charge Density Magnetic Moments Energetic Quantities 11.18 Magnetic Anisotropy The Non-Relativistic Limit, the RKKY Interaction The Orion of Anisotropy
12 Electrons and Photons 12.1 Photon Polarization and Angular Momentum 12.2 Quantizing the Electromagnetic Field 12.3 Time-Dependent Perturbation Theory 12.4 Photon Absorption and Emission in Condensed Matter 12.5 Magneto-Optical Effects 12.6 Photon Scattering Theory 12.7 Thomson Scattering 12.8 Rayleigh Scattering 12.9 Compton Scattering 12.10 Magnetic Scattering of X-Rays 12.11 Resonant Scattering of X-Rays 13 Superconductivity 13.1 Do Electrons Find Each Other Attractive? 13.2 Superconductivity, the Hamiltonian 13.3 The Dirac--Bogolubov-de Gennes Equation 13.4 Solution of the Dirac-Bogolubov-de Gennes Equations 13.5 Observable Properties of Superconductors 13.6 Elcctrodynamics of Superconductors Appendix A The Uncertainty Principle Appendix B The Confluent Hypergeometrie Function B.1 Relations to Other Functions Appendix C Spherical Harmonics Appendix D Unit Systems Appendix E Fundamental Constants References Index
