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About Mathematical Methods Quantum Mechanics
Abstract. This book provides a self-contained introduction to mathematical methods in quantum mechanics (spectral theory) with applications to Schrodinger operators. The rst 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 Schrodinger operator respectively position, momentum and angular momentum operators. Then we develop Weyl{Titchmarsh theory for Sturm{Liouville operators and apply it to spherically symmetric problems, in particular to the hydrogen atom. Next we investigate self-adjointness of atomic Schrodinger 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. Schrodinger operators, quantum mechanics, unbounded operators, spectral theory. Typeset by AMS-LATEX and Makeindex. Version: December 8, 2008 Copyright c 1999{2008 by Gerald Teschl
Detailed Information
| Author: | ['mojicap'] |
|---|---|
| Publication Year: | 2008 |
| Pages: | 314 |
| Language: | English |
| Format: | |
| Price: | FREE |
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