“他山之石，可以攻玉”，为了满足国内读者对国外优秀物理学著作的需求，科学出版社出版了“国外物理名著系列”，本书为该系列第25册，《量子物理中的格林函数(影印版第3版)》，既有阐述学科基本理论的经典名著，也有反映某一学科专题前沿的专著。该丛书基础理论方面的图书强调“经典”，选择了那些经得起时间检验、对物理学的发展产生重要影响、现在还不“过时”的著作，反映物理学某一领域进展的著作强调“前沿”和“热点”，相信这套丛书的出版能够为国内物理学工作者和青年学生的工作和学习提供参考。

The main part of this book is devoted to the simplest kind of Green's functions，namely the solutions of linear differential equations with a delta function source. It is shown that these familiar Green's functions are a powerful tool for obtaining relatively simple and general solutions of basic quantum problems such as scattering and bound-level information. The bound-level treatment gives a clear physical understanding of“difficult”questions such as superconductivity，the Kondo effect，and，to a lesser degree，disorder-induced localization. The more advanced subject of many-body Green's functions is presented in the last part of the book.

Part Ⅰ Green's Functions in Mathematical Physics

 1 Time-Independent Green's Functions

1.1 Formalism

1.2 Examples

 1.2.1 Three-Dimensional Case (d=3)

 1.2.2 Two-Dimensional Case (d=2)

 1.2.3 One-Dimensional Case (d=1)

 1.2.4 Finite Domain (2

1.3 Summary

 1.3.1 Definition

 1.3.2 Basic Properties

 1.3.3 Methods of Calculation

 1.3.4 Use

Further Reading

Problems

 2 Time-Dependent Green's Functions

2.1 First-Order Case

 2.1.1 Examples

2.2 Second-Order Case

 2.2.1 Examples

2.3 Summary

 2.3.1 Definition

 2.3.2 Basic Properties

 2.3.3 Definition

 2.3.4 Basic Properties

 2.3.5 Use

Further Reading

Problems

Part Ⅱ Green's Functions in One-Body Quantum Problems

 3 Physical Significance of G.Application to the Free-Particle Case

3.1 General Relations

3.2 The Free-Particle (Ho=p2/2m) Case

 3.2.1 3-d Case

 3.2.2 2-d Case

 3.2.3 1-d Case

3.3 The Free-Particle Klein Gordon Case

3.4 Summary

Further Reading

Problems

 4 Green's Functions and Perturbation Theory

4.1 Formalism

 4.1.1 Time-Independent Case

 4.1.2 Time-Dependent Case

4.2 Applications

 4.2.1 Scattering Theory (E>0)

 4.2.2 Bound State in Shallow Potential Wells (E<0)

 4.2.3 The KKR Method for Electronic Calculations in Solids.

4.3 Summary

Further Reading

Problems

 5 Green's Functions for Tight-Binding Hamiltonians

5.1 Introductory Remarks

5.2 The Tight-Binding Hamiltonian (TBH)

5.3 Green's Functions

 5.3.1 One-Dimensional Lattice

 5.3.2 Square Lattice

 5.3.3 Simple Cubic Lattice

 5.3.4 Green's Functions for Bethe Lattices (Cayley Trees)

5.4 Summary

Further Reading

Problems

 6 Single Impurity Scattering

6.1 Formalism

6.2 Explicit Results for a Single Band

 6.2.1 Three-Dimensional Case

 6.2.2 Two-Dimensional Case

 6.2.3 One-Dimensional Case

6.3 Applications

 6.3.1 Levels in the Gap

 6.3.2 The Cooper Pair and Superconductivity

 6.3.3 The Kondo Problem

 6.3.4 Lattice Vibrations in Crystals Containing "Isotope" Impurities

6.4 Summary

Further Reading

Problems

 7 Two or More Impurities; Disordered Systems

7.1 Two Impurities

7.2 Infinite Number of Impurities

 7.2.1 Virtual Crystal Approximation (VCA)

 7.2.2 Average t-Matrix Approximation (ATA)

 7.2.3 Coherent Potential Approximation (CPA)

 7.2.4 The CPA for Classical Waves

 7.2.5 Direct Extensions of the CPA

 7.2.6 Cluster Generalizations of the CPA

7.3 Summary

Further Reading

Problems

 8 Electrical Conductivity and Green's Functions

8.1 Electrical Conductivity and Related Quantities

8.2 Various Methods of Calculation

 8.2.1 Phenomenological Approach

 8.2.2 Boltzmann's Equation

 8.2.3 A General, Independent-Particle Formula for Conductivity

 8.2.4 General Linear Response Theory

8.3 Conductivity in Terms of Green's Functions

 8.3.1 Conductivity Without Vertex Corrections

 8.3.2 CPA for Vertex Corrections

 8.3.3 Vertex Corrections Beyond the CPA

 8.3.4 Post-CPA Corrections to Conductivity

8.4 Summary

Further Reading

Problems

 9 Localization, Transport, and Green's Functions

9.1 An Overview

9.2 Disorder, Diffusion, and Interference

9.3 Localization

 9.3.1 Three-Dimensional Systems

 9.3.2 Two-Dimensional Systems

 9.3.3 One-Dimensional and Quasi-One-Dimensional Systems

9.4 Conductance and Transmission

9.5 Scaling Approach

9.6 Other Calculational Techniques

 9.6.1 Quasi-One-Dimensional Systems and Scaling

 9.6.2 Level Spacing Statistics

9.7 Localization and Green's Functions

 9.7.1 Green's Function and Localization in One Dimension .

 9.7.2 Renormalized Perturbation Expansion (RPE) and Localization

 9.7.3 Green's Functions and Transmissions in Quasi-One-Dimensional Systems

9.8 Applications

9.9 Summary

Further Reading

Problems

Part Ⅲ Green's Functions in Many-Body Systems

 10 Definitions

10.1 Single-Particle Green's Functions in Terms of Field Operators

10.2 Green's Functions for Interacting Particles

10.3 Green's Functions for Noninteracting Particles

10.4 Summary

Further Reading

Problems

 11 Properties and Use of the Green's Functions

11.1 Analytical Properties of gs and gs

11.2 Physical Significance and Use of gs and gs

11.3 Quasiparticles

11.4 Summary

 11.4.1 Properties

 11.4.2 Use

Further Reading

Problems

 12 Calculational Methods for g

12.1 Equation of Motion Method

12.2 Diagrammatic Method for Fermions at T=0

12.3 Diagrammatic Method for T≠0

12.4 Partial Summations. Dyson's Equation

12.5 Other Methods of Calculation

12.6 Summary

Further Reading

Problems

 13 Applications

13.1 Normal Fermi Systems. Landau Theory

13.2 High-Density Electron Gas

13.3 Dilute Fermi Gas

13.4 Superconductivity

 13.4.1 Diagrammatic Approach

 13.4.2 Equation of Motion Approach

13.5 The Hubbard Model

13.6 Summary

Further Reading

Problems

 A Dirac's delta Function

 B Dirac's bra and ket Notation

 C Solutions of Laplace and Helmholtz Equations in Various Coordinate Systems

C.1 Helmholtz Equation

 C.1.1 Cartesian Coordinates

 C.1.2 Cylindrical Coordinates

 C.1.3 Spherical coordinates

C.2 Vector Derivatives

 C.2.1 Spherical Coordinates

 C.2.2 Cylindrical Coordinates

C.3 Schrodinger Equation in Centrally Symmetric 3-and 2-Dimensional Potential V

D Analytic Behavior of G(z) Near a Band Edge

E Wannier Functions

F Renormalized Perturbation Expansion (RPE)

G Boltzmann's Equation

H Transfer Matrix, S-Matrix, etc

I Second Quantization

Solutions of Selected Problems

References

Index