相对论量子力学

出版社: 世界图书出版公司; 第1版 (2008年8月1日)

丛书名: 经典英文物理学教材系列

平装: 594页

正文语种: 简体中文, 英语

开本: 16

ISBN: 9787506292580

条形码: 9787506292580

尺寸: 25.6 x 18.4 x 2.8 cm

重量: 998 g

作者：(英国)斯诸哲 (Strange.P.)

《相对论量子力学》是一部介绍相对论量子理论的研究生教程，重在强调其在凝聚态物理中的重要应用。基本理论包括：狭义相对论，角动量和零自旋粒子；文章讨论了Dirac 方程，对称和算子以及自由粒子，黑洞和Klein矛盾也被提及，并且解决了一些模型问题；紧接着主要量子理论在凝聚态物质中的应用，单电子原子爆炸的相对理论，并将该理论发展来描述多粒子系统的量子力学，包括Hartree-Fock和密度函数法。散射理论，带结构，磁光效应和超导。书中配有不少练习题。

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

《相对论量子力学》为经典英文物理学教材系列之一，由世界图书出版公司出版。

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I always thought I would write a book and this is it. In the end, though, hardly wrote it at all, it evolved from my research notes, from essays I wrote for postgraduates starting work with me, and from lecture handouts I distribute to students taking the relativistic quantum mechanics option in

the Physics department at Keele University. Therefore the early chapters of this book discuss pure relativistic quantum mechanics and the later chapters discuss applications of relevance in condensed matter physics. This book, then, is written with an audience ranging from advanced students to professional researchers in mind. I wrote it because anyone aiming to do research in relativistic quantum theory applied to condensed matter has to pull together information from a wide range of sources using different conventions, notation and units, which can lead to a lot of confusion (I speak from experience). Most relativistic quantum mechanics books, it seems to me, are directed towards quantum field theory and particle physics, not condensed matter physics, and many start off at too advanced a level for present day physics graduates from a British university. Therefore, I have tried to start at a sufficiently elementary level, and have used the SI system of units throughout.