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Determining Spectra in Quantum Theory

  • Livre Relié
  • 232 Nombre de pages
The spectral theory of Schrödinger operators, in particular those with random potentials, continues to be a very active field of r... Lire la suite
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Description

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 a 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 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 because of its contribution to works in spectral theory.

Texte du rabat

This work focuses on various known criteria in the spectral theory of selfadjoint operators. The concise, unified presentation is aimed at graduate students and researchers working in the spectral theory of Schrodinger operators with either fixed or random potentials. But given the large gap this book fills in the literature, it will serve a wider audience of mathematical physicists in its contribution to works in spectral theory.



Contenu

* Preface * Measures and Transforms > Measures > Fourier Transform > The Wavelet Transform > Borel Transform > Gesztesy-Krein-Simon 'E' Function > Notes * Selfadjointness and Spectrum > Selfadjointness > Spectrum and Resolvent Sets > Spectral Theorem > Spectrol Measures and Spectrum > Spectral Theorem in the Hahn-Hellinger Form > Components of the Spectrum > Characterization of the States in Spectral Subspaces > Notes * Criteria for Identifying the Spectrum > Borel Transform > Fourier Transform > Wavelet Transform > Eigenfunctions > Commutators > Criteria Using Scattering Theory > Notes * Operators of Interest > Unperturbed Operators > Perturbed Operators > Notes * Applications > Borel Transforms > Scattering > Notes * References * Index

Détails sur le produit

Titre: Determining Spectra in Quantum Theory
Auteur:
Code EAN: 9780817643669
ISBN: 978-0-8176-4366-9
Format: Livre Relié
Editeur: Birkhäuser Boston
Genre: Mathématique
nombre de pages: 232
Poids: 514g
Taille: H235mm x B155mm x T18mm
Année: 2005
Auflage: 2005