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 quantum mechanics, in particular the analysis of Schrödinger operators and quantum scattering theory. The final two chapters are devoted to Mourre's conjugate operator method and some of its consequences for scattering theory. The text gives complete proofs and includes numerous exercises.

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 lecturers of basic and advanced quantum mechanics and to mathematical physicists in general, including those who work in spectral and scattering theory.

Hilbert Spaces - Linear Operators - Symmetric Operators and their Extensions - Spectral Theory of Self-Adjoint Operators - Evolution Groups and Scattering Theory - The Conjugate OperatorMethod - Further Topics in Scattering Theory - References - Notation Index - Subject Index

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