# Quantum Mechanics

## 3rd Edition

### Non-Relativistic Theory

**Authors:**L D Landau E. M. Lifshitz

**eBook ISBN:**9781483149127

**Imprint:**Pergamon

**Published Date:**23rd May 1977

**Page Count:**688

## Description

Quantum Mechanics, Third Edition: Non-relativistic Theory is devoted to non-relativistic quantum mechanics. The theory of the addition of angular momenta, collision theory, and the theory of symmetry are examined, together with spin, nuclear structure, motion in a magnetic field, and diatomic and polyatomic molecules. This book is comprised of 18 chapters and begins with an introduction to the basic concepts of quantum mechanics, with emphasis on the uncertainty principle, the principle of superposition, and operators, as well as the continuous spectrum and the wave function. The following chapters explore energy and momentum; Schrödinger's equation; angular momentum; and motion in a centrally symmetric field and in a magnetic field. Perturbation theory, spin, and the properties of quasi-classical systems are also considered. The remaining chapters deal with the identity of particles, atoms, and diatomic and polyatomic molecules. The final two chapters describe elastic and inelastic collisions. This monograph will be a valuable source of information for physicists.

## Table of Contents

- Other Titles in the Course of Theoretical Physics
- FROM THE PREFACE TO THE FIRST ENGLISH EDITION
- PREFACE TO THE SECOND ENGLISH EDITION
- PREFACE TO THE THIRD RUSSIAN EDITION
- NOTATION
- Chapter 1: THE BASIC CONCEPTS OF QUANTUM MECHANICS
- Publisher Summary
- §1. The uncertainty principle
- §2. The principle of superposition
- §3. Operators
- §4. Addition and multiplication of operators
- §5. The continuous spectrum
- §6. The passage to the limiting case of classical mechanics
- §7. The wave function and measurements

- Chapter 2: ENERGY AND MOMENTUM
- Publisher Summary
- §8. The Hamiltonian operator
- §9. The differentiation of operators with respect to time
- §10. Stationary states
- §11. Matrices
- §12. Transformation of matrices
- §13. The Heisenberg representation of operators
- §14. The density matrix
- §15. Momentum
- §16. Uncertainty relations

- Chapter 3: SCHRÖDINGER’S EQUATION
- Publisher Summary
- §17. Schrödinger’s equation
- §18. The fundamental properties of Schrödinger’s equation
- §19. The current density
- §20. The variational principle
- §21. General properties of motion in one dimension
- §22. The potential well
- §23. The linear oscillator
- §24. Motion in a homogeneous field
- §25. The transmission coefficient

- Chapter 4: ANGULAR MOMENTUM
- Publisher Summary
- §26. Angular momentum
- §27. Eigenvalues of the angular momentum
- §28. Eigenfunctions of the angular momentum
- §29. Matrix elements of vectors
- §30. Parity of a state
- §31. Addition of angular momenta

- Chapter 5: MOTION IN A CENTRALLY SYMMETRIC FIELD
- Publisher Summary
- §32. Motion in a centrally symmetric field
- §33. Spherical waves
- §34. Resolution of a plane wave
- §35. Fall of a particle to the centre
- §36. Motion in a Coulomb field (spherical polar coordinates)
- §37. Motion in a Coulomb field (parabolic coordinates)

- Chapter 6: PERTURBATION THEORY
- Publisher Summary
- §38. Perturbations independent of time
- §39. The secular equation
- §40. Perturbations depending on time
- §41. Transitions under a perturbation acting for a finite time
- §42. Transitions under the action of a periodic perturbation
- §43. Transitions in the continuous spectrum
- §44. The uncertainty relation for energy
- §45. Potential energy as a perturbation

- Chapter 7: THE QUASI-CLASSICAL CASE
- Publisher Summary
- §46. The wave function in the quasi-classical case
- §47. Boundary conditions in the quasi-classical case
- §48. Bohr and Sommerfeld’s quantization rule
- §49. Quasi-classical motion in a centrally symmetric field
- §50. Penetration through a potential barrier
- §51. Calculation of the quasi-classical matrix elements
- §52. The transition probability in the quasi-classical case
- §53. Transitions under the action of adiabatic perturbations

- Chapter 8: SPIN
- Publisher Summary
- §54. Spin
- §55. The spin operator
- §56. Spinors
- §57. The wave functions of particles with arbitrary spin
- §58. The operator of finite rotations
- §59. Partial polarization of particles
- §60. Time reversal and Kramers’ theorem

- Chapter 9: IDENTITY OF PARTICLES
- Publisher Summary
- §61. The principle of indistinguishability of similar particles
- §62. Exchange interaction
- §63. Symmetry with respect to interchange
- §64. Second quantization. The case of Bose statistics
- §65. Second quantization. The case of Fermi statistics

- Chapter 10: THE ATOM
- Publisher Summary
- §66. Atomic energy levels
- §67. Electron states in the atom
- §68. Hydrogen-like energy levels
- §69. The self-consistent field
- §70. The Thomas–Fermi equation
- §71. Wave functions of the outer electrons near the nucleus
- §72. Fine structure of atomic levels
- §73. The Mendeleev periodic system
- §74. X-ray terms
- §75. Multipole moments
- §76. An atom in an electric field
- §77. A hydrogen atom in an electric field

- Chapter 11: THE DIATOMIC MOLECULE
- Publisher Summary
- §78. Electron terms in the diatomic molecule
- §79. The intersection of electron terms
- §80. The relation between molecular and atomic terms
- §81. Valency
- §82. Vibrational and rotational structures of singlet terms in the diatomic molecule
- §83. Multiplet terms. Case a
- §84. Multiplet terms. Case b
- §85. Multiplet terms. Cases c and d
- §86. Symmetry of molecular terms
- §87. Matrix elements for the diatomic molecule
- §88. Λ-doubling
- §89. The interaction of atoms at large distances
- §90. Pre-dissociation

- Chapter 12: THE THEORY OF SYMMETRY
- Publisher Summary
- §91. Symmetry transformations
- §92. Transformation groups
- §93. Point groups
- §94. Representations of groups
- §95. Irreducible representations of point groups
- §96. Irreducible representations and the classification of terms
- §97. Selection rules for matrix elements
- §98. Continuous groups
- §99. Two-valued representations of finite point groups

- Chapter 13: POLYATOMIC MOLECULES
- Publisher Summary
- §100. The classification of molecular vibrations
- §101. Vibrational energy levels
- §102. Stability of symmetrical configurations of the molecule
- §103. Quantization of the rotation of a top
- §104. The interaction between the vibrations and the rotation of the molecule
- §105. The classification of molecular terms

- Chapter 14: ADDITION OF ANGULAR MOMENTA
- Publisher Summary
- §106. 3j-symbols
- §107. Matrix elements of tensors
- §108. 6j-symbols
- §109. Matrix elements for addition of angular momenta
- §110. Matrix elements for axially symmetric systems

- Chapter 15: MOTION IN A MAGNETIC FIELD
- Publisher Summary
- §111. Schrödinger’s equation in a magnetic field
- §112. Motion in a uniform magnetic field
- §113. An atom in a magnetic field
- §114. Spin in a variable magnetic field
- §115. The current density in a magnetic field

- Chapter 16: NUCLEAR STRUCTURE
- Publisher Summary
- §116. Isotopic invariance
- §117. Nuclear forces
- §118. The shell model
- §119. Non-spherical nuclei
- §120. Isotopic shift
- §121. Hyperfine structure of atomic levels
- §122. Hyperfine structure of molecular levels

- Chapter 17: ELASTIC COLLISIONS
- Publisher Summary
- §123. The general theory of scattering
- §124. An investigation of the general formula
- §125. The unitary condition for scattering
- §126. Bora’s formula
- §127. The quasi-classical case
- §128. Analytical properties of the scattering amplitude
- §129. The dispersion relation
- §130. The scattering amplitude in the momentum representation
- §131. Scattering at high energies
- §132. The scattering of slow particles
- §133. Resonance scattering at low energies
- §134. Resonance at a quasi-discrete level
- §135. Rutherford’s formula
- §136. The system of wave functions of the continuous spectrum
- §137. Collisions of like particles
- §138. Resonance scattering of charged particles
- §139. Elastic collisions between fast electrons and atoms

- Chapter 18: INELASTIC COLLISIONS
- Publisher Summary
- §142. Elastic scattering in the presence of inelastic processes
- §143. Inelastic scattering of slow particles
- §144. The scattering matrix in the presence of reactions
- §145. Breit and Wigner’s formulae
- §146. Interaction in the final state in reactions
- §147. Behaviour of cross-sections near the reaction threshold
- §148. Inelastic collisions between fast electrons and atoms
- §149. The effective retardation
- §150. Inelastic collisions between heavy particles and atoms
- §151. Scattering of neutrons
- §152. Inelastic scattering at high energies

- MATHEMATICAL APPENDICES
- INDEX

## Details

- No. of pages:
- 688

- Language:
- English

- Copyright:
- © Pergamon 1977

- Published:
- 23rd May 1977

- Imprint:
- Pergamon

- eBook ISBN:
- 9781483149127

## About the Author

### L D Landau

### Affiliations and Expertise

Institute of Physical Problems, U.S.S.R. Academy of Sciences