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.

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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.

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