The authors investigate a class of solvable models for quantum mechanics given by a Schrödinger Hamiltonian with potential supported on a discrete (finite or infinite) set of points or "sources." Their general topics include the one-center point interaction, point interactions with a finite number of centers, and point interactions with infinitely many centers. This second edition of the original publication of 1988 has been slightly expanded and corrected. The authors include an appendix (aptly entitled "Seize ans après" ) that contains updated information and its own bibliography. Annotation ©2004 Book News, Inc., Portland, OR (booknews.com)
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Helge Holden is Professor of Mathematics at the Norwegian University of Science and Technology.
"There is a wealth of very pretty examples of Schrödinger operators here." -- MathSciNet
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Hardback. Condition: New. 2nd. This monograph presents a detailed study of a class of solvable models in quantum mechanics that describe the motion of a particle in a potential having support at the positions of a discrete (finite or infinite) set of point sources. Both situations-where the strengths of the sources and their locations are precisely known and where these are only known with a given probability distribution-are covered. The authors present a systematic mathematical approach to these models and illustrate its connections with previous heuristic derivations and computations. Results obtained by different methods in disparate contexts are thus unified and a systematic control over approximations to the models, in which the point interactions are replaced by more regular ones, is provided.The first edition of this book generated considerable interest for those learning advanced mathematical topics in quantum mechanics, especially those connected to the Schrodinger equations. This second edition includes a new appendix by Pavel Exner, who has prepared a summary of the progress made in the field since 1988. His summary, centering around two-body point interaction problems, is followed by a bibliography focusing on essential developments made since 1988. appendix by Pavel Exner, who has prepared a summary of the progress made in the field since 1988. His summary, centering around two-body point interaction problems, is followed by a bibliography focusing on essential developments made since 1988. The material is suitable for graduate students and researchers interested in quantum mechanics and Schrodinger operators. Seller Inventory # LU-9780821836248
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