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.