Quantum mechanical problems capable of exact solution are traditionally solved in a few instances only (such as the harmonic oscillator and angular momentum) by operator methods, but mainly by means of Schrodinger's wave mechanics. The present volume shows that a large range of one- and three- dimensional problems, including certain relativistic ones, are solvable by algebraic, representation-independent methods using commutation relations, shift operators, the viral, hyperviral, and Hellman-Feynman theorems. Applications of these operator methods to the calculation of eigenvalues, matrix elements, and wavefunctions are discussed in detail. This volume provides an outstanding introduction to the use of operator methods in quantum mechanics, and also serves as a reference work on this topic. As such it is an excellent complement to senior and graduate courses in quantum mechanics. Although primarily a book on applications of operator methods, the presentation is made
self-contained by the inclusion of an introductory chapter on the formalism of quantum mechanics. Additional background material supplements the volume at various points in the text. Although there has been much research on operator methods to solve quantum mechanical problems, until now many of these results have remained scattered throughout the literature. Nonspecialists, as well as graduate and upper division students in physics will find this accessible volume to be essential reading in theoretical physics.
Industry Reviews
'van Fraassen's exploration of the interpretation of the models used by quantum mechanics is just as relevant to realists (if not more so) ... Few technicalities are left unexplained; all the needed group theory, measure theory, and so on, is introduced along the way with van Fraassen's characteristic clarity ... I must confess to finding Quantum Mechanics the best I have read yet. I can see myself wandering through its pages again and again.'
Times Higher Education Supplement
'this book will certainly become a valuable and informative reference on the use of operator methods in one-body (and two-body) quantum mechanics ... It will also provide a useful source of supplementary reading for students whose main exposure to quantum mechanics has been via the most elementary and naive approach due to Schrödinger.'
Professor R.F. Bishop, UMIST, Contemporary Physics, Volume 33, Number 3, 1992
'van Fraasen introduces each topic with care and attention to detail ... Quantum Mechanics is a thought-provoking and largely well-written monograph expressing the author's philosophical view of quantum mechanics. The work is complemented by an extensive bibliography containing important contributions by numerous authors.'
Dr S.M. Barnett, University of Strathclyde, Contemporary Physics, Volume 34, Number 2, March/April 1993
