量子物理中的格林函數(英文版)

量子物理中的格林函數(英文版)
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內容簡介

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.
 

目錄

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 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
……
Part Ⅲ Green﹀s Functions in Many-Body Systems
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