TY  - BOOK
AU  - Demuth,Michael
AU  - Krishna,Maddaly
ED  - SpringerLink (Online service)
TI  - Determining Spectra in Quantum Theory
T2  - Progress in Mathematical Physics
SN  - 9780817644390
U1  - 515.96 23
PY  - 2005///
CY  - Boston, MA
PB  - Birkhäuser Boston
KW  - MATHEMATICS
KW  - FUNCTIONAL ANALYSIS
KW  - OPERATOR THEORY
KW  - DIFFERENTIAL EQUATIONS, PARTIAL
KW  - POTENTIAL THEORY (MATHEMATICS)
KW  - QUANTUM THEORY
KW  - MATHEMATICAL PHYSICS
KW  - POTENTIAL THEORY
KW  - MATHEMATICAL METHODS IN PHYSICS
KW  - QUANTUM PHYSICS
KW  - PARTIAL DIFFERENTIAL EQUATIONS
N1  - Measures and Transforms -- Selfadjointness and Spectrum -- Criteria for Identifying the Spectrum -- Operators of Interest -- Applications
N2  - 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
UR  - http://dx.doi.org/10.1007/0-8176-4439-3
ER  -