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Green's functions in quantum physics / Eleftherios N. Economou.



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Economou, E. N., 1940-
Publication date:
3rd [expanded] ed. - Berlin ; New York : Springer, c2006.
  • Book
  • xvii, 477 p. : ill. ; 25 cm.
Includes bibliographical references (p. [447]-460) and index.
  • 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.
  • (source: Nielsen Book Data)
Publisher's Summary:
This 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 percent longer than the previou and offers end-of-chapter problems and solutions (40 percent 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.
(source: Nielsen Book Data)
Springer series in solid-state sciences, 0171-1873 ; 7
Springer series in solid-state sciences ; 7.

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