# Quantum Mechanics

## 2nd Edition

### International Series in Natural Philosophy

**Author:**A. S. Davydov

**Editor:**D. ter Haar

**eBook ISBN:**9781483187839

**Imprint:**Pergamon

**Published Date:**1st January 1965

**Page Count:**652

## Description

Quantum Mechanics, Second Edition discusses the fundamental concepts and governing principles of quantum mechanics. The title details the physical ideas and the mathematical formalism of the quantum theory of the non-relativistic and quasi-relativistic motion of a single particle in an external field.
The text first covers the basic concepts, and then proceeds to tackling the change of quantum states in time. Next, the selection examines the connection between quantum mechanics and classical mechanics. The book also discusses the simplest applications of quantum mechanics, along with the elementary representation theory.

The book will be most useful to students of physics who are studying quantum mechanics. The text will also serve expert quantum physicists as a reference.

## Table of Contents

Preface

Preface to Second Edition

Preface to the English Edition

Chapter I. The Basic Concepts of Quantum Mechanics

1. Introduction

2. The Wave-function of a Free Particle

3. The Principle of Superposition of States: Wave-packets

4. Statistical Interpretation of the Wave-function

5. Free Particle in a Bounded Volume in Space

6. Calculation of the Average Values of the Coordinate and the Momentum

7. Operators Corresponding to Physical Quantities

8. Eigenfunctions and Eigenvalues of Operators

9. Properties of the Eigenfunctions of Operators with a Discrete Spectrum

10. Properties of the Eigenfunctions of Operators with a Continuous Spectrum

11. The Conditions under Which Several Physical Quantities can have Well-defined Values in the Same State

12. Methods to Determine the States of Quantum Systems

13. The Heisenberg Relations for Physical Quantities

14. Description of States by Means of the Density Matrix

Problems

Chapter II. Change of Quantum States in Time

15. The Schrödinger Wave Equation

16. Stationary States

17. Change in Time of Average Values of Physical Quantities

18. Integrals of Motion and Symmetry Conditions

19. Group Theory in Quantum Mechanics

20. Change with Time of States Described by a Density Matrix

Problems

Chapter III. The Connexion between Quantum Mechanics and Classical Mechanics

21. The Limiting Transition from Quantum to Classical Mechanics

22. Semi-classical Approximation

23. The Bohr-Sommerfeld Quantization Rules

24. Passage through a Potential Barrier: Motion of a Particle over a Potential Barrier or over a Potential Well

Problems

Chapter IV. The Simplest Applications of Quantum Mechanics

25. A Particle in a Rectangular Potential Well

26. The Harmonic Oscillator

Problems

Chapter V. Elementary Representation Theory

27. Different Representations of the State Vector

28. Different Representations of Operators

29. The Determination of the Eigenfunctions and Eigenvalues of Operators Given in the Form of Matrices

30. The General Theory of Unitary Transformations

31. Unitary Transformations Corresponding to a Change of State with Time

32. Occupation Number Representation for the Harmonic Oscillator

33. The Occupation Number Representation for the Vibrations of Atoms in a One-dimensional Crystal

Problems

Chapter VI. The Motion of Aparticle in Acentral Field of Force

34. General Properties of the Motion of a Particle in a Spherically Symmetric Field

35. Free Motion with a Well-defined Value of the Orbital Angular Momentum

36. Motion in a Spherically Symmetric Rectangular Potential Well

37. Spherically Symmetric Oscillator Well

38. Motion in a Coulomb Field; the Discrete Spectrum

39. Motion in a Coulomb Field; the Continuous Spectrum

40. Angular Momentum Operator

41. Vector Addition of Two Angular Momenta

42. Vector Addition of Three Angular Momenta; Racah Coefficients

43. Transformation of the Eigenfunctions of the Angular Momentum Operators under a Rotation of the Coordinate Axes

44. The Generalized Spherical Functions as Eigenfunctions of the Angular Momentum Operator

45. Rotation of a Rigid Body; The Symmetrical Top

46. Rotation of a Rigid Body; The Asymmetrical Top

Problems

Chapter VII. Approximate Methods for Evaluating Eigenvalues and Eigenfunctions

47. Perturbation Theory for Stationary Discrete States of a Spectrum

48. Conditions for the Applicability of Perturbation Theory

49. Perturbation Theory when Two Levels are Close

50. Perturbation Theory for Degenerate Levels

51. Applications of the Variational Method to Approximate Calculations

52. The Method of Canonical Transformations

Problems

Chapter VIII. The Foundations of Aquasi-relativistic Quantum Theory of the Motion of Aparticle in an External Field

53. Elementary Particles in Quantum Mechanics

54. Relativistic Equation for a Zero-spin Particle

55. Free Spin-zero Particles

56. Free Zero-spin Particles in the Feshbach-Villars Representation

57. Integrals of Motion and Eigenvalues of Operators in a Relativistic Theory of a Zero-spin Particle

58. Interaction of a Spin-zero Particle with an Electromagnetic Field

59. Dirac's Relativistic Equation

60. Free Motion of Particles Described by the Dirac Equation

61. Covariant form of the Dirac Equation

62. The Angular Momentum of the Electron in the Dirac Theory

63. Relativistic Corrections to the Motion of an Electron in an Electromagnetic Field

64. Spin-orbit Interaction

65. Charge Conjugation; Particles and Antiparticles

66. The Dirac Equation for a Zero-rest-mass Particle; The Neutrino

67. The Hydrogen Atom, Taking the Electron Spin into Account

68. Exact Solution of the Dirac Equation for a Coulomb Field

69. Atom in an External Magnetic Field

70. Atom in an External Electric Field

Problems

Chapter IX. Quantum Theory of Systems Consisting of Identical Particles

71. The Schrodinger Equation for a System Consisting of Identical Particles

72. Symmetric and Antisymmetric Wavefunctions

73. Elementary Theory of the Ground State of Two-electron Atoms

74. Excited States of the Helium Atom; Ortho- and Para-helium

75. Self-consistent Hartree-Fock Field

76. The Statistical Thomas-Fermi Method

77. The Periodic System

78. Spectral and X-ray Terms

79. The Shell Model of the Atomic Nucleus

Problems

Chapter X. Second Quantization of Systems of Identical Bosons

80. Second Quantization of the Electromagnetic Field without Charges

81. Photons with a Well-defined Angular Momentum and Parity

82. Phonons in a Three-dimensional Crystal

83. Second Quantization of the Meson Field

84. Quasi-particles in a System of Interacting Bosons

85. Basic Ideas of a Microscopic Theory of Super-fluidity

Problems

Chapter XI. Second Quantization of Systems of Identical Fermions

86. Occupation Number Representation for Systems of Non-interacting Fermions

87. Systems of Fermions Interacting through Pair Forces; Bogolyubov's Canonical Transformation

88. The Interaction of Electrons with the Phonons in a Metal and the Microscopic Theory of Superconductivity

89. Quantization of the Electron-positron Field

Problems

Chapter XII. The Theory of Quantum Transitions under the Influence of an External Perturbation

90. A General Expression for the Probability of a Transition from One State to Another

91. Excitation of an Atom through Bombardment by a Heavy Particle

92. Adiabatic and Sudden Switching on and Switching off of the Interaction

93. Transition Probability Per Unit Time

94. The Interaction of a Quantum System with Electromagnetic Radiation

95. Selection Rules for the Emission and Absorption of Light; Multi-pole Radiation

96. Lifetime of Excited States and Width of Energy Levels

97. Linear Response of a Quantum System to an External Agent

98. Polarizability of a Quantum System

99. Elementary Theory of the Photo-effect

100. Transitions Caused by Time-independent Interactions

101. Probability for Quantum Transitions and the S-matrix

Problems

Chapter XIII. Quantum Theory of Relaxation Processes

102. The Statistical Operator of a Dynamical Subsystem

103. The Simplest Model of a Quantum System Interacting with a Thermostat

104. The Probability for the Transfer of Excitation Energy from a Donor to an Acceptor when a Dissipative Medium is Present

105. The Fluctuation-dissipation Theorem for the Generalized Susceptibility

Problems

Chapter XIV. Quantum Theory of Scattering

106. Elastic Scattering of Spin-zero Particles

107. The Free Particle Green Function

108. Theory of Elastic Scattering in the Born Approximation

109. Partial Wave Method in Scattering Theory

110. Elastic Scattering of Slow Particles

111. Elastic Scattering in a Coulomb Field

112. Exchange Effects in Elastic Scattering of Identical Spin-zero Particles

113. Exchange Effects in Elastic Scattering of Identical Particles with Spin

114. General Theory of Inelastic Scattering

115. Scattering of an Electron by an Atom, Neglecting Exchange

116. Theory of Collisions Involving Rearrangements of Particles; Reactions

117. Scattering of an Electron by a Hydrogen Atom, Including Exchange

118. The Scattering Matrix

119. Time Reversal and Detailed Balancing

120. Scattering of Slow Neutrons by Atomic Nuclei

121. Scattering of Polarized Nucleons and Polarization of Nucleons when Scattered by Zero-spin Nuclei

122. Theory of Scattering when Two Kinds of Interaction are Present; Distorted Wave Approximation

123. Dispersion Relations in Scattering Theory

124. The Scattering Matrix in the Complex Angular Momentum Plane

125. Potential and Resonance Scattering

126. Coherent and Incoherent Scattering of Slow Neutrons

127. Coherent Scattering of Neutrons by Crystalline Substances

128. Elastic Scattering of Slow Neutrons by Crystals, Including Atomic Vibrations

Problems

Chapter XV. Elementary Theory of Molecules and Chemical Bonds

129. Theory of the Adiabatic Approximation

130. The Hydrogen Molecule

131. Elementary Theory of Chemical Forces

132. Classification of Molecular Electronic States When the Positions of the Nuclei are Fixed

133. Nuclear Vibrations in Molecules

134. Rotational Energy of Molecules

135. Types of Coupling of Angular Momenta in Molecules

136. Molecular Spectra; Franck-Condon Principle

Problems

Mathematical Appendices

A. Some Properties of the Dirac Delta-function

B. The Angular Momentum Operators in Spherical Coordinates

C. Linear Operators in a Vector Space; Matrices

D. Confluent Hypergeometric Functions; Bessel Functions

E. Group Theory

Index

## Details

- No. of pages:
- 652

- Language:
- English

- Copyright:
- © Pergamon 1965

- Published:
- 1st January 1965

- Imprint:
- Pergamon

- eBook ISBN:
- 9781483187839

## About the Author

### A. S. Davydov

### Affiliations and Expertise

Member of Ukrainian Academy of Science