Description
Book SynopsisPresents 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. This title is suitable for graduate students and researchers interested in quantum mechanics and Schrodinger operators.
Table of ContentsIntroduction The one-center point interaction: The one-center point interaction in three dimensions Coulomb plus one-center point interaction in three dimensions The one-center $\delta$-interaction in one dimension The one-center $\delta$'-interaction in one dimension The one-center 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: Self-adjoint extensions of symmetric operators Spectral properties of Hamiltonians defined as quadratic forms Schrodinger operators with interactions concentrated around infinitely many centers Boundary conditions for Schrodinger operators on $(0,\infty)$ Time-dependent 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 apres Bibliography Errata and addenda.
