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Quantum Mechanics
International Series in Natural Philosophy
- 2nd Edition - January 1, 1965
- Author: A. S. Davydov
- Editor: D. ter Haar
- Language: English
- eBook ISBN:9 7 8 - 1 - 4 8 3 1 - 8 7 8 3 - 9
Quantum Mechanics, Second Edition discusses the fundamental concepts and governing principles of quantum mechanics. The title details the physical ideas and the mathematical… Read more
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Request a sales quoteQuantum 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.
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
- No. of pages: 652
- Language: English
- Edition: 2
- Published: January 1, 1965
- Imprint: Pergamon
- eBook ISBN: 9781483187839
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A. S. Davydov
Affiliations and expertise
Member of Ukrainian Academy of ScienceRead Quantum Mechanics on ScienceDirect