Operator Methods in Quantum Mechanics

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

• ISBN13: 9780198539612
• ISBN10: 0198539614
• Format: Hardcover
• Copyright: 1992-01-09
• Publisher: Clarendon Press

Summary

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.

Table of Contents

The Mathematical Formalism of Quantum Mechanics

The Harmonic Oscillator

Other One-Dimensional Systems

Angular Momentum

Spherically Symmetric Potentials

Applications

Factorizations with Applications 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

Relativistic Quantum Mechanics

Relativistic Spherically Symmetric Problems

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