Quantum Mechanics

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