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Green's Functions in Quantum Physics

'Springer Series in Solid-State Sciences'. Sprache: Englisch.
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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 relati … weiterlesen
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Green's Functions in Quantum Physics als Buch


Titel: Green's Functions in Quantum Physics
Autor/en: Eleftherios N. Economou

ISBN: 3540288384
EAN: 9783540288381
'Springer Series in Solid-State Sciences'.
Sprache: Englisch.
Springer, Berlin

27. Juni 2006 - gebunden - 480 Seiten


In this third edition the book has been expanded in three directions: 1. Problems have been added at the end of each chapter (40% of which are solved in the last section of the book) together with suggestions for further reading. Furthermore, the number of appendices (marked with a grey stripe) has been substantially enlarged in order to make the book more self-su?cient. These additions, together with many clari?cations in the text, render the book more suitable as a companion in a course on Green's functions and their applications. 2. Theimpressivedevelopmentsofthe1980sand1990sinmesoscopicphysics, and in particular in transport properties, found their way - to a c- tain extent - in the new Chaps.8 and 9 (which also contain some of the material of the old Chap.7). This is a natural expansion, since Green's functions have played an important role as a theoretical tool in this new ?eld of physics, a role that continues in nanoregime research (see, e.g., recent publications dealing with carbon nanotubes). Thus, the powerful and unifying formalism of Green's functions ?nds applications not only in standard physics subjects such as perturbation and scattering theory, bound-state formation, etc., but also at the forefrontof current and, most likely, future developments. 3. Over the last 15 yearsor so Green's functions havefound applications not only in condensed matter electronicmotion but in classicalwavepropa- tion in both periodic and random media; photonic and phononic crystals aretheoutcomesofthislineofresearchwhoseunderlyingbasictheoretical principles are summarized in Sect.7.2.4.


Green's Functions in Mathematical Physics.- Time-Independent Green's Functions.- Time-Dependent Green's Functions.- Green's Functions in One-Body Quantum Problems.- Physical Significance of G. Application to the Free-Particle Case.- Green's Functions and Perturbation Theory.- Green's Functions for Tight-Binding Hamiltonians.- Single Impurity Scattering.- Two or More Impurities; Disordered Systems.- Electrical Conductivity and Green's Functions.- Localization, Transport, and Green's Functions.- Green's Functions in Many-Body Systems.- Definitions.- Properties and Use of the Green's Functions.- Calculational Methods for g.- Applications.


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)
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