Operator Methods in Quantum Mechanics - Hardcover

De Lange, O. L.; Raab, R. E.

Hardcover

ISBN 10: 0198539614 ISBN 13: 9780198539612

Publisher: Clarendon Press, 1991

Synopsis

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 virial, hypervirial, and Hellman-Feyman theorems. Applications of these operator methods to the calculation of eigenvalues, matrix elements, and wavefunctions are discussed in detail.

This book is an introduction to the use of operator methods in quantum mechanics and also a reference work with numerous problmes solved. It is suitable for use by students of intermediate quantum mechanics and also more advanced postgraduate students who wish to study the algebraic method of solving quantum mechanical problems.

About this title

Product Description

The purpose of this volume is two-fold; to provide an introduction to the use of operator methods in quantum mechanics and to serve as a reference work on this topic. As such it should be suitable for use as a complement to senior and graduate courses in quantum mechanics. Although this is primarily a book on applications of operator methods, the presentation is made self-contained by including an introductory chapter on the formalism on quantum mechanics and by giving some background material at various points in the text. Although there has been much research on operator methods to solve quantum mechanical problems many of these results have remained scattered in the literature and therefore somewhat inaccessible to the non-specialist until now.

Review

'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

Edition details

• Publisher: Clarendon Press
• Publication date: 1991
• Language: English
• ISBN 10: 0198539614
• ISBN 13: 9780198539612
• Binding: Hardcover
• Number of pages: 390