Exercises in Quantum Mechanics: A Collection of Illustrative Problems and Their Solutions

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Springer Science & Business Media, 1992 - Mathematics - 333 pages
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This monograph is written within the framework of the quantum mechanical paradigm. It is modest in scope in that it is restricted to some observations and solved illustrative problems not readily available in any of the many standard (and several excellent) texts or books with solved problems that have been written on this subject. Additionally a few more or less standard problems are included for continuity and purposes of comparison. The hope is that the points made and problems solved will give the student some additional insights and a better grasp of this fascinating but mathematically somewhat involved branch of physics. The hundred and fourteen problems discussed have intentionally been chosen to involve a minimum of technical complexity while still illustrating the consequences of the quantum-mechanical formalism. Concerning notation, useful expressions are displayed in rectangular boxes while calculational details which one may wish to skip are included in square brackets. Beirut HARRY A. MAVROMATIS June, 1985 IX Preface to Second Edition More than five years have passed since I prepared the first edition of this mono graph. The present revised edition is more attractive in layout than its predecessor, and most, if not all of the errors in the original edition (many of which were kindly pointed out by reviewers, colleagues, and students) have now been corrected. Additionally the material in the original fourteen chapters has been extended with significant additions to Chapters 8, 13, and 14.
 

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Contents

WilsonSommerfeld Quantization Condition
1
The Delta Function Completeness and Closure
16
Momentum Space
34
Wavepackets and the Uncertainty Principle
47
Uncertainty Principle and GroundState Energies of QuantumMechanical Systems
68
Free Particles Incident on Potentials Time Delay Phase Shifts and The Born Approximation
74
Heisenberg Representation
102
Two Three and N Versus OneDimensional Problems
111
Perturbation Theory
157
Degeneracy
186
The Inverse Problem
214
The DalgarnoLewis Technique
227
Angular Momentum and Coupled States
262
Tensor Operators and Evaluation of Matrix Elements
291
Applications of Quantum Mechanics
312
Index
326

Kramers Type Expressions The Virial Theorem and Generalizations
124
Upper Bounds and Parity Considerations
133

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Page iii - Department of Physics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia Kluwer Academic Publishers Dordrecht / Boston / London by • "CIP-data available from the Publisher on request.

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