Determining Spectra in Quantum Theory

Michael Demuth, M. Krishna - Collection Progress in Mathematical Physics

220 pages, parution le 12/10/2005

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Résumé

The spectral theory of Schrödinger operators, in particular those with random potentials, continues to be a very active field of research. This work focuses on various known criteria in the spectral theory of selfadjoint operators in order to identify the spectrum and its components à la Lebesgue decomposition. Key features and topics:

Well-developed exposition of criteria that are especially useful in determining the spectra of deterministic and random Schrödinger operators occurring in quantum theory
Systematically uses measures and their transforms (Fourier, Borel, wavelet) to present a unifying theme
Establishes criteria for identifying the spectrum
Examines a series of applications to show point spectrum and continuous spectrum in some models of random operators
Presents a series of spectral-theoretic results for the perturbed operators introduced in the earlier chapters with examples of localization and delocalization in the theory of disordered systems
Presents modern criteria (using wavelet transform, eigenfunction decay) that could be used to do spectral theory
Unique work in book form combining the presentation of the deterministic and random cases, which will serve as a platform for further research activities

This concise unified presentation is aimed at graduate students and researchers working in the spectral theory of Schrödinger operators with either fixed or random potentials in particular. However, given the large gap that this book fills in the literature, it will serve a wider audience of mathematical physicists in its contribution to works in spectral theory.

Written for: Graduate students and researchers working in the spectral theory of Schrödinger

Sommaire

Measures and transforms
Selfadjointness and spectrum
Criteria for identifying the spectrum
Operators of Interest
Applications

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	PAPIER
Éditeur(s)	Birkhäuser
Auteur(s)	Michael Demuth, M. Krishna
Collection	Progress in Mathematical Physics
Parution	12/10/2005
Nb. de pages	220
Format	16 x 24
Couverture	Relié
Poids	465g
Intérieur	Noir et Blanc
EAN13	9780817643669
ISBN13	978-0-8176-4366-9