The 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 monograph generated considerable  interest for those learning advanced mathematical topics in  quantum mechanics, especially those connected to the  Schr?dinger 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. The material is suitable for graduate students and researchers  interested in quantum mechanics and Schr?dinger operators.

Solvable Models in Quantum Mechanics With Appendix Written By Pavel Exner, Second Edition (AMS Chelsea Publishing) PDF

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