Synopses & Reviews
The new edition of a standard reference will be of interest to advanced students wishing to become familiar with the method of Green's functions for obtaining simple and general solutions to basic problems in quantum physics. The main part is devoted to the simplest kind of Green's functions, namely the solutions of linear differential equations with a -function source. It is shown that these familiar Green's functions are a powerful tool for obtaining relatively simple and general solutions of basic problems such as scattering and boundlevel 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. This third edition is 50% longer than the previou and offers end-of-chapter problems and solutions (40% are solved) and additional appendices to helpit is to serve as an effective self-tutorial and self-sufficient reference. Throughout, it demonstrates the powerful and unifying formalism of Green's functions across many applications, including transport properties, carbon nanotubes, and photonics and photonic crystals.
Review
From the reviews of the third edition: "The main purpose of this book is to provide graduate students, and also experienced researchers, with a clear and quite detailed survey of the applications of Green's functions in different modern fields of quantum physics. ... In summary, this book is a good manual for people who want to understand the physics and the various applications of Green's functions in modern fields of physics. It can also be used as a starting point for studying numerical analysis in condensed matter theory." (Jean-Yves-Fortin, Mathematical Reviews, Issue, 2007 i)
Synopsis
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 -function source. It is shown that these familiar Green's functions are a powerful tool for obtaining relatively simple and general solutions of basic 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.
Table of Contents
1. Time-Independent Green's Functions.- 2. Time-Dependent Green's Functions.- 3. Physical Significance of G. Application to the Free-Particle Case.- 4. Green's Functions and Perturbation Theory.- 5. Green's Functions for Tight-Binding Hamiltonians.- 6. Single Impurity Scattering.- 7. Two or More Impurities; Disordered Systems.- 8. Electrical Conductivity and Green's Functions.- 9. Localization, Transport, and Green's Functions.- 10. Definitions.- 11. Properties and Use of the Green's Functions.- 12. Calculational Methods for g.- 13. Applications.- Appendices: A. Dirac's delta Function.- B. Dirac's bra and ket Notation.- C. Solutions of Laplace and Helmholtz Equations in Various Coordinate Systems.- D. Analytic Dehavior of G(z) Near a Band Edge.- E. The Wannier Functions.- F. The Renormalized Pertubation Expansion (RPE).- G. Boltzmann's Equations.- H. Transfer Matrix, S-Matrix, etc.- I. Second Quantization.