Non-Fiction Books:

C0-Groups, Commutator Methods and Spectral Theory of N-Body Hamiltonians

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C0-Groups, Commutator Methods and Spectral Theory of N-Body Hamiltonians by Werner O Amrein
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Description

The relevance of commutator methods in spectral and scattering theory has been known for a long time, and numerous interesting results have been ob- tained by such methods. The reader may find a description and references in the books by Putnam [Pu], Reed-Simon [RS] and Baumgartel-Wollenberg [BW] for example. A new point of view emerged around 1979 with the work of E. Mourre in which the method of locally conjugate operators was introduced. His idea proved to be remarkably fruitful in establishing detailed spectral properties of N-body Hamiltonians. A problem that was considered extremely difficult be- fore that time, the proof of the absence of a singularly continuous spectrum for such operators, was then solved in a rather straightforward manner (by E. Mourre himself for N = 3 and by P. Perry, 1. Sigal and B. Simon for general N). The Mourre estimate, which is the main input of the method, also has consequences concerning the behaviour of N-body systems at large times. A deeper study of such propagation properties allowed 1. Sigal and A. Soffer in 1985 to prove existence and completeness of wave operators for N-body systems with short range interactions without implicit conditions on the potentials (for N = 3, similar results were obtained before by means of purely time-dependent methods by V. Enss and by K. Sinha, M. Krishna and P. Muthuramalingam). Our interest in commutator methods was raised by the major achievements mentioned above.
Release date Australia
February 29th, 1996
Country of Publication
Switzerland
Edition
2nd Revised edition
Illustrations
XIV, 464 p.
Imprint
Birkhauser Verlag AG
Pages
464
Dimensions
156x234x26
ISBN-13
9783764353650
Product ID
2811240

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