Operator methods in quantum mechanics


Operator methods in quantum mechanics

O.L. De Lange and R.E. Raab

(Oxford science publications)

Clarendon Press , Oxford University Press, 1991

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Includes bibliographical references and indexes



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.


  • 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.

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