Exercises in Quantum Mechanics

1. Front Matter

   Pages i-xiii

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2. Wilson-Sommerfeld Quantization Condition

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   Pages 1-15

3. The Delta Function, Completeness, and Closure

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   Pages 16-33

4. Momentum Space

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   Pages 34-46

5. Wavepackets and the Uncertainty Principle

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   Pages 47-67

6. Uncertainty Principle and Ground-State Energies of Quantum-Mechanical Systems

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   Pages 68-73

7. Free Particles Incident on Potentials, Time Delay, Phase Shifts, and the Born Approximation

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   Pages 74-101

8. Heisenberg Representation

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   Pages 102-110

9. Two-, Three-, and N-, Versus One-Dimensional Problems

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   Pages 111-123

10. ‘Kramers’ Type Expressions, the Virial Theorem, and Generalizations

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    Pages 124-132

11. Upper Bounds and Parity Considerations

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    Pages 133-156

12. Perturbation Theory

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    Pages 157-185

13. Degeneracy

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    Pages 186-213

14. The Inverse Problem

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    Pages 214-226

15. The Dalgarno-Lewis Technique

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    Pages 227-261

16. Angular Momentum and Coupled States

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    Pages 262-290

17. Tensor Operators, and Evaluation of Matrix Elements

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    Pages 291-311

18. Applications of Quantum Mechanics

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    Pages 312-325

19. Back Matter

    Pages 326-335

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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.

• Mathematica
• algebra
• complexity
• illustration
• mechanics
• particles
• perturbation theory
• phase
• physics
• quantization
• quantum mechanics

• Department of Physics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia

  Harry Mavromatis

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