Operator Methods in Quantum Mechanics

ISBN-13: 9780198539612 / Angielski / Twarda / 1991 / 390 str.

O. L. de Lange; R. E. Raab

Opis

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.

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. Although there has been much research on this, many of these results have remained scattered in the literature and therefore somewhat inaccessible to the non-specialist until now.

Recenzje

'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

Spis treści

Preface; The mathematical formalism of quantum mechanics; The harmonic oscillator; Other one-dimensional systems; Angular momentum; Spherically symmetric potentials; Applications; Factorization with application to the momentum representation; The isotropic harmonic oscillator in an angular momentum basis; The Coulomb problem in an angular momentum basis; The Coulomb problem in the basis /HA OzL Tz; Relativistic quantum mechanics; Relativistic spherically symmetric problems; References; Appendices.