相对论量子力学

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　Blochs 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　Greens Functions
11.2　Time-Dependent Greens Functions
11.3　The T-Operator
11.4　The Relativistic Free-Particle Greens 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 Greens Function
11.11 Transforming Between Representations
11.12 The Scattering Path Operator
11.13 The Non-Relativistic Free Particle Greens Function
11.14 Multiple Scattering Theory
11.15 The Multiple Scattering Greens 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