Hilbert Space Methods in Quantum Mechanics

Linear operators in Hilbert space play a fundamental role in the formulation of quantum theory. This book offers a self-contained presentation of the most important tools and methods from Hilbert space theory, with particular focus on the spectral theory of self-adjoint operators. But it also goes further by describing some applications in quantunm mechanics, in particular the analysis of Schrodinger operators and quantunm scattering theory. The final two chap- ters are devoted to Mourre's conjugate operator method and some of its con- sequences for scattering theory. Based on a one-year course offered to advanced undergraduates, the text will be especially useful to students with some background in quantum mechanics, to whom it will provide a fundamental treatment of some of the basic ideas of applied Hilbert space theory; in addition, the book will prove invaluable to lec- turers of basic and advanced quantum mechanics and to mathematical physi- cists in general, including those who work in spectral and scattering theory. The text gives complete proofs and includes numerous exercises.