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 situationswhere the strengths of the sources and their locations are precisely known and where these are only known with a given probability distributionare 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 Schrödinger 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 twobody 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 twobody 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 Schrödinger operators. Readership Graduate students and research mathematicians interested in quantum mechanics and Schrödinger operators. Reviews "There is a wealth of very pretty examples of Schrödinger operators here which could be presented ... in an elementary quantum mechanics course."  MathSciNet Table of Contents The onecenter point interaction  The onecenter point interaction in three dimensions
 Coulomb plus onecenter point interaction in three dimensions
 The onecenter \(\delta\)interaction in one dimension
 The onecenter \(\delta\)'interaction in one dimension
 The onecenter point interaction in two dimensions
Point interactions with a finite number of centers  Finitely many point interactions in three dimensions
 Finitely many \(\delta\)interactions in one dimension
 Finitely many \(\delta\)'interactions in one dimension
 Finitely many point interactions in two dimensions
Point interactions with infinitely many centers  Infinitely many point interactions in three dimensions
 Infinitely many \(\delta\)interactions in one dimension
 Infinitely many \(\delta\)'interactions in one dimension
 Infinitely many point interactions in two dimensions
 Random Hamiltonians with point interactions
Appendices  Selfadjoint extensions of symmetric operators
 Spectral properties of Hamiltonians defined as quadratic forms
 Schrödinger operators with interactions concentrated around infinitely many centers
 Boundary conditions for Schrödinger operators on \((0,\infty)\)
 Timedependent scattering theory for point interactions
 Dirichlet forms for point interactions
 Point interactions and scales of Hilbert spaces
 Nonstandard analysis and point interactions
 Elements of probability theory
 Relativistic point interactions in one dimension
 References
 Author Index
 Subject Index
 Seize ans après
 Bibliography
 Errata and addenda
