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Green’s Functions in Quantum Physics

  • Book
  • © 1983

Overview

Authors:
  1. Eleftherios N. Economou

    1. Department of Physics, University of Crete, Heraklion, Crete, Greece

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

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Table of contents (11 chapters)

  1. Front Matter

    Pages I-XIV
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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

      • Eleftherios N. Economou
      Pages 3-18

    3. Time-Dependent Green’s Functions

      • Eleftherios N. Economou
      Pages 19-35

  3. Green’s Functions in One-Body Quantum Problems

    1. Front Matter

      Pages 37-37
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    2. Physical Significance of G. Application to the Free Particle Case

      • Eleftherios N. Economou
      Pages 39-49

    3. Green’s Functions and Perturbation Theory

      • Eleftherios N. Economou
      Pages 50-70

    4. Green’s Functions for Tight-Binding Hamiltonians

      • Eleftherios N. Economou
      Pages 71-96

    5. Single Impurity Scattering

      • Eleftherios N. Economou
      Pages 97-127

    6. Two or More Impurities; Disordered Systems

      • Eleftherios N. Economou
      Pages 128-195

  4. Green’s Functions in Many-Body Systems

    1. Front Matter

      Pages 197-197
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    2. Definitions

      • Eleftherios N. Economou
      Pages 199-214

    3. Properties and Use of the Green’s Functions

      • Eleftherios N. Economou
      Pages 215-238

    4. Calculational Methods for g

      • Eleftherios N. Economou
      Pages 239-264

    5. Applications

      • Eleftherios N. Economou
      Pages 265-281
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Keywords

About this book

In this edition the second and main part of the book has been considerably expanded as to cover important applications of the formalism. In Chap.5 a section was added outlining the extensive role of the tight­ binding (or equivalently the linear combination of atomic-like orbitals) approach to many branches of solid-state physics. Some additional informa­ tion (including a table of numerical values) regarding square and cubic lattice Green's functions were incorporated. In Chap.6 the difficult subjects of superconductivity and the Kondo effect are examined by employing an appealingly simple connection to the question of the existence of a bound state in a very shallow potential well. The existence of such a bound state depends entirely on the form of the un­ perturbed density of states near the end of the spectrum: if the density of states blows up there is always at least one bound state. If the density of states approaches zero continuously, a critical depth (and/or width) of the well must be reached in order to have a bound state. The borderline case of a finite discontinuity (which is very important to superconductivity and the Kondo effect) always produces a bound state with an exponentially small binding energy.

Authors and Affiliations

  • Department of Physics, University of Crete, Heraklion, Crete, Greece

    Eleftherios N. Economou

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