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This book is a thorough and systematic exposition of the foundations of non-relativistic quantum mechanics and is designed for a first-time study of the subject.

The first chapter is an introduction to quantum mechanics through analysis of the specific character of microscopic physics. In the second chapter, based upon the concept of amplitude probability, various questions on physics of microphenomena are considered (interference of amplitudes, superposition principle, specificity of measuring act, causality in quantum mechanics). The simplest quantum mechanical systems ---microobjects with two basic states--- are analyzed in detail. In the third chapter we take a look at quantum mechanical methods as a synthesis of physical ideas and the theory of linear operators. Some specially selected examples and problems are presented to demonstrate the application of this methods.

This book is intended for students of technical and pedagogical universities, and can also be used by engineers of different specialities.


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Contents


Preface
Prelude. Can the System of Classical Physics Concepts Be Considered Logically Perfect?
1 Physics of the Microparticles
1. Certain Characteristics and Properties of Microparticles
2. Two Fundamental Ideas of Quantum Mechanics
3. Uncertainty Relations
4. Some Results Ensuing from the Uncertainty Relations
5. Impossibility of Classical Representation of a Microparticle
6. Rejection of Ideas of Classical Physics
Interlude. Is a "Physically Intuitive" Model of a Microparticle Possible?
2 Physical Foundations of Quantum Mechanics
7. Some Basic Experiments
8. Amplitudes of Transition Probabilities (Formulation of Basic Principles)
9. Amplitudes of Transition Probabilities (Demonstration of Basic Principles)
10. Superposition of States
11. Measurement in Quantum Mechanics
Interlude. Are These the Same Waves? Or, Again on Waves in Quantum Mechanics
12. Causality in Quantum Mechanics
13. Microparticles with Two Basic States
14. The Electron in a Magnetic Field
15. The Wave Function
16. Quantum Mechanics as a Qualitative Leap in Man's Knowledge of the Laws of Nature
Interlude. Do Quantum-Mechanical Concepts Contradict Our Common Sense?
3 Linear Operators in Quantum Mechanics
17. A Brief Look at the Theory of Linear Operators
18. From Hamiltonian Matrix to Energy Operator
19. Linear Operators in Quantum Mechanics
20. The Quantum-Mechanical Apparatus in Coordinate Representation
21. Applications of the Schredinger Equation
22. The Hamiltonian in Some Specific Problems
23. Transition to the Momentum Representation
24. An Electron in a Periodic Field
25. The Probability of Quantum Transitions
26. Ways of Describing Evolution of Microsystems with Time
On the History of Origin and Growth of Quantum Mechanics (A Brief Historical Survey)
Appendix A. Eigenvalues and Eigenfunctions of a Hermitian Operator
Appendix B. Transition from Quantum Mechanics to Classical Mechanics
Appendix C. Commutation Relations
Appendix D. Commutation of Operators M2 and Mi
Appendix E. Some Special Functions
Appendix F. Linear Harmonic Oscillators
Bibliography