Economou Green’s Functions in Quantum Physics

2. Auflage 1983
ISBN: 978-3-662-02369-3
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 7, 316 Seiten, eBook

Reihe: Springer Series in Solid-State Sciences

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.

Zielgruppe

Research

Autoren/Hrsg.

Economou, Eleftherios N.

Inhaltsverzeichnis

I: Green’s Functions in Mathematical Physics.- 1. Time-Independent Green’s Functions.- 2. Time-Dependent Green’s Functions.- II: Green’s Functions in One-Body Quantum Problems.- 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 liamiltonians.- 6. Single Impurity Scattering.- 7. Two or More Impurities; Disordered Systems.- III: Green’s Functions in Many-Body Systems.- 8. Definitions.- 9. Properties and Use of the Green’s Functions.- 10. Calculational Methods for g.- 11. Applications.- References.