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Green's Functions in Quantum Physics

  • Book
  • © 2006

Overview

Authors:
  1. Eleftherios N. Economou

    1. Foundation for Research and Technology-Hellas (FORTH), Department of Physics, University of Crete, Heraklion, Crete, Greece

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  • Long-established and respected reference on a key mathematical methods in physics (first published in 1979).
  • Substantially expanded 3rd edition (50% longer) now offers end-of-chapter problems and solutions (40% are solved) and additional appendices to serve as a self-tutorial and self-sufficient reference.
  • Demonstrates the powerful and unifying formalism of Green's functions with many applications, including transport properties, carbon nanotubes, and photonics and phoontic crystals.
  • Includes supplementary material: sn.pub/extras

Part of the book series: Springer Series in Solid-State Sciences (SSSOL, volume 7)

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Table of contents (13 chapters)

  1. Front Matter

    Pages I-XVII
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  2. Green’s Functions in Mathematical Physics

    1. Front Matter

      Pages 1-1
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    2. Time-Independent Green’s Functions

      Pages 3-19

    3. Time-Dependent Green’s Functions

      Pages 21-37

  4. Green’s Functions in Many-Body Systems

    1. Front Matter

      Pages 247-247
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    2. Definitions

      Pages 249-262

    3. Properties and Use of the Green’s Functions

      Pages 263-283

    4. Calculational Methods for g

      Pages 285-308

    5. Applications

      Pages 309-335

  5. Back Matter

    Pages 337-477
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Keywords

About this book

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.

Reviews

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)

Authors and Affiliations

  • Foundation for Research and Technology-Hellas (FORTH), Department of Physics, University of Crete, Heraklion, Crete, Greece

    Eleftherios N. Economou

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