Spectral theory of random Schrödinger operators
a genectic introduction
by Reinhard Lang
The interplay between the spectral theory of Schr|dinger operators and probabilistic considerations forms the main theme of these notes, written for the non-specialist reader and intended to provide a brief and elementaryintroduction to this field. An attempt is made to show basic ideas in statu nascendi and to follow their evaluation from simple beginnings through to more advanced results. The term "genetic" in the title refers to this proceedure. The author concentrates on 2 topics which, in the history of the subject, have been of major conceptual importance - on the one hand the Laplacian is a random medium and the left end of its spectrum (leading to large deviation problems for Brownian motion and the link to thenotion of entropy) and on the other, Schr|dinger operators with general ergodic potentials in one-dimensional space. Ideas and concepts are explained in the simplest, possible setting and by means of a few characteristic problems with heuristic arguments preceding rigorous proofs.
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Subjects
Random operators, Schrödinger operator, Spectral theory (Mathematics), Schrödinger, Opérateur de, Spektraltheorie, Spectre (Mathématiques), Zufälliger Hamilton-Operator, Operadores (analise funcional), Schrodinger equation, Mathematics, Distribution (Probability theory), Mathematical physics| Edition | Availability |
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1
Spectral Theory of Random Schrödinger Operators: A Genetic Introduction
2006, Springer London, Limited
in English
3540466274 9783540466277
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2
Spectral theory of random Schrödinger operators: a genectic introduction
1991, Springer-Verlag
in English
3540549757 9783540549758
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Edition Notes
Includes bibliographical references (p. [119]-121) and index.
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