Quantum Mechanics

Quantum Mechanics

International Series in Natural Philosophy

2nd Edition - January 1, 1965

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  • Author: A. S. Davydov
  • eBook ISBN: 9781483187839

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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


    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


    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


    Chapter IV. The Simplest Applications of Quantum Mechanics

    25. A Particle in a Rectangular Potential Well

    26. The Harmonic Oscillator


    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


    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


    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


    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


    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


    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


    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


    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


    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


    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


    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


    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


Product details

  • No. of pages: 652
  • Language: English
  • Copyright: © Pergamon 1965
  • Published: January 1, 1965
  • Imprint: Pergamon
  • eBook ISBN: 9781483187839

About the Author

A. S. Davydov

Affiliations and Expertise

Member of Ukrainian Academy of Science

About the Editor

D. ter Haar

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