Hilbert Space Methods in Quantum Mechanics
Werner O. Amrein
EFPL Press
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.