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

This monograph is written within the framework of the quantum mechanical paradigm. It is modest in scope in that it is restricted to some obser­ vations 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 illus­ trating 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.

1 / Wilson-Sommerfeld Quantization Condition.- 2 / The Delta Function, Completeness and Closure.- 3 / Momentum Space.- 4 / Wavepackets and the Uncertainty Principle.- 5 / Uncertainty Principle and Ground-State Energies of Quantum-Mechanical Systems.- 6 / Free Particles Incident on Potentials, Time Delay, Phase Shiffs and the Born Approximation.- 7 / Heisenberg Representation.- 8 / Two and Three Versus One-Dimensional Problems.- 9 / ‘Kramer’ Type Expressions. The Virial Theorem and Generalizations.- 10 / Upper Bounds and Parity Considerations.- 11 / Perturbation Theory.- 12 / Degeneracy.- 13 / The Inverse problem.- 14 / The Dalgarno-Lewis Technique.