Comments:

316 pages, 2009, to appear as volume 99 in the GSM series of the American Mathematical

Abstract:

The book "provides a self-contained introduction to mathematical methods in quantum mechanics (spectral theory) with applications to Schroedinger operators. The first part covers mathematical foundations of quantum mechanics from self-adjointness, the spectral theorem, quantum dynamics (including Stone's and the RAGE theorem) to perturbation theory for self-adjoint operators. The second part starts with a detailed study of the free Schroedinger operator respectively position, momentum and angular momentum operators. Then the Weyl-Titchmarsh theory for Sturm--Liouville operators is developed and and applied to spherically symmetric problems, in particular to the hydrogen atom. Next we investigate self-adjointness of atomic Schroedinger operators and their essential spectrum, in particular the HVZ theorem. Finally, we have a look at scattering theory and prove asymptotic completeness in the short range case." Keywords and phrases. Schroedinger operators, quantum mechanics, unbounded operators, spectral theory. Typeset by AMS-LATEX and Makeindex. Version: January 4, 2009 http://www.mat.univie.ac.at/~gerald/ftp/book-schroe/schroe.pdf

Rights:

Open access and free download online at: http://www.mat.univie.ac.at/~gerald/ftp/book-schroe/schroe.pdf Copyright@1999 -2008 by Gerald Teschl.

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