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 Nom-Relativistic Limit of the Dirac Equation

4.5 An Alternative Formulation of the Dirac Equation

4.6 Prlbabilities and Currents

4.7 Gordon Decomposition

4.8 Forces and Fields

4.9 Gauge Invariance and the Dirac Equation

4.10 Problems

5 Free Particles/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

5.5 Problems

6 Symmetries and Operators

6.1 Nom-Relativistic Spin Projecrtion Operators

6.2 Relativistic Energy and Spin Projection Operators

6.3 Charge Conjugation

6.4 Time-Reversal Invariance

6.5 Parity

6.6 …

6.7 Angular Momentum Again

6.8 Non-Relativistic Limits Again

6.9 Second Quantization

……

7 Separating Particles from Antiparticles

8 One-Electrom Atoms

9 Potential Problems

10 More Than One Electron

11 Scattering Theory

12 Electrons and Photons

13 Superconductivity

Appendix A The Uncertainty Principle

Appendix B The Confluent Hypergeometric Function

B.1 Relations to Other Functions

Appendix C Spherical Harmonics

Appendix D Unit Systems

Appendix E Fundamental Constants

References

Index

Unlike so many other supportive families, mine did not proof-read, or type this manuscript, or anything else. In fact they played absolutely mo part in the preparation of this book, and distracted me from it at every opportunity. They are not the slightest bit interested in physics and know nothing of relativity and quantum theory. Their lack of knowledge in these areas does not worry them at all. Furthermore they undermine one of the central tenets of the theory of relativity, by providing me with aunique frame of reference. Nonetheless, I would like to dedicate this book to them, Jo,Jessica, Susanna and Elizabeth.