# Quantum Mechanics

### A Shorter Course of Theoretical Physics

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Quantum Mechanics deals with various aspects of quantum mechanics and covers topics ranging from the uncertainty principle and the principle of superposition to conservation laws, Schrödinger's equation, and perturbation theory. Spin, radiation, and the identity of particles are also discussed, along with the atom, the diatomic molecule, elastic and inelastic collisions, and Feynman diagrams. Comprised of 16 chapters, this volume begins with an overview of non-relativistic quantum theory and the basic concepts of quantum mechanics such as the principles of uncertainty and superposition, operators, and the density matrix. Subsequent chapters deal with conservation laws in quantum mechanics; Schrödinger's equation and general properties of its solutions; perturbations independent of time and dependent on time; spin and the spin operator; and the principle of indistinguishability of similar particles. The atom and its electron states are also examined, together with diatomic molecules; elastic and inelastic collisions; photons and electrons; Dirac's equation; and particles and antiparticles. The final chapter is devoted to Feynman diagrams, paying particular attention to the scattering matrix, radiative corrections, and radiative shift of atomic levels. This book will be of interest to physicists.

## Table of Contents

- A Shorter Course of Theoretical Physics: IN THREE VOLUMES
- PREFACE
- PUBLISHER’S NOTE
- NOTATION
- Part I: Non-relativistic theory
- 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 density matrix

- Chapter 2: CONSERVATION LAWS IN QUANTUM MECHANICS
- Publisher Summary
- §8. The Hamiltonian operator
- §9. The differentiation of operators with respect to time
- §10. Stationary states
- §11. Matrices of physical quantities
- §12. Momentum
- §13. Uncertainty relations
- §14. Angular momentum
- §15. Eigenvalues of the angular momentum
- §16. Eigenfunctions of the angular momentum
- §17. Addition of angular momenta
- §18. Angular momentum selection rules
- §19. Parity of a state

- Chapter 3: SCHRÖDINGER’S EQUATION
- Publisher Summary
- §20. Schrödinger’s equation
- §21. The current density
- §22. General properties of solutions of Schrödinger’s equation
- §23. Time reversal
- §24. The potential well
- §25. The linear oscillator
- §26. The quasi-classical wave function
- §27. Bohr and Sommerfeld’s quantisation rule
- §28. The transmission coefficient
- §29. Motion in a centrally symmetric field
- §30. Spherical waves
- §31. Motion in a Coulomb field

- Chapter 4: PERTURBATION THEORY
- Publisher Summary
- §32. Perturbations independent of time
- §33. The secular equation
- §34. Perturbations depending on time
- §35. Transitions in the continuous spectrum
- §36. Intermediate states
- §37. The uncertainty relation for energy
- §38. Quasi-stationary states

- Chapter 5: SPIN
- Publisher Summary
- §39. Spin
- §40. The spin operator
- §41. Spinors
- §42. Polarisation of electrons
- §43. A particle in a magnetic field
- §44. Motion in a uniform magnetic field

- Chapter 6: IDENTITY OF PARTICLES
- Publisher Summary
- §45. The principle of indistinguishability of similar particles
- §46. Exchange interaction
- §47. Second quantisation. The case of Bose statistics
- §48. Second quantisation. The case of Fermi statistics

- Chapter 7: THE ATOM
- Publisher Summary
- §49. Atomic energy levels
- §50. Electron states in the atom
- §51. Fine structure of atomic levels
- §52. The Mendeleev periodic system
- §53. X-ray terms
- §54. An atom in an electric field
- §55. An atom in a magnetic field

- Chapter 8: THE DIATOMIC MOLECULE
- Publisher Summary
- §56. Electron terms in the diatomic molecule
- §57. The intersection of electron terms
- §58. Valency
- §59. Vibrational and rotational structures of terms in the diatomic molecule
- §60. Parahydrogen and orthohydrogen
- §61. Van der Waals forces

- Chapter 9: ELASTIC COLLISIONS
- Publisher Summary
- §62. The scattering amplitude
- §63. The condition for quasi-classical scattering
- §64. Discrete energy levels as poles of the scattering amplitude
- §65. The scattering of slow particles
- §66. Resonance scattering at low energies
- §67. Born’s formula
- §68. Rutherford’s formula
- §69. Collisions of like particles
- §70. Elastic collisions between fast electrons and atoms

- Chapter 10: INELASTIC COLLISIONS
- Publisher Summary
- §71. The principle of detailed balancing
- PROBLEMS†
- §72. Elastic scattering in the presence of inelastic processes
- §73. Inelastic scattering of slow particles
- §74. Inelastic collisions between fast particles and atoms

- Chapter 1: THE BASIC CONCEPTS OF QUANTUM MECHANICS
- Part II: Relativistic theory
- Chapter 11: PHOTONS
- Publisher Summary
- §75. The uncertainty principle in the relativistic case
- §76. Quantisation of the free electromagnetic field†
- §77. Photons
- §78. The angular momentum and parity of the photon

- Chapter 12: DIRAC’S EQUATION
- Publisher Summary
- §79. The Klein–Fock equation
- §80. Four-dimensional spinors
- §81. Inversion of spinors
- §82. Dirac’s equation
- §83. Dirac matrices
- §84. The current density in Dirac’s equation

- Chapter 13: PARTICLES AND ANTIPARTICLES
- Publisher Summary
- §85. Ψ-operators
- §86. Particles and antiparticles
- §87. The relation between the spin and the statistics
- §88. Strictly neutral particles
- §89. Internal parity of particles
- §90. The CPT theorem
- §91. Neutrinos

- Chapter 14: ELECTRONS IN AN EXTERNAL FIELD
- Publisher Summary
- §92. Dirac’s equation for an electron in an external field
- §93. Magnetic moment of the electron‡
- §94. Spin-orbit interaction

- Chapter 15: RADIATION
- Publisher Summary
- §95. The electromagnetic interaction operator
- §96. Spontaneous and stimulated emission†
- §97. Dipole radiation
- §98. Multipole radiation
- §99. Radiation from atoms†
- §100. The infra-red catastrophe
- §101. Scattering of radiation
- §102. Natural width of spectral lines

- Chapter 16: FEYNMAN DIAGRAMS
- Publisher Summary
- §103. The scattering matrix
- §104. Feynman diagrams
- §105. Radiative corrections
- §106. Radiative shift of atomic levels

- Chapter 11: PHOTONS
- INDEX

## Product details

- No. of pages: 382
- Language: English
- Copyright: © Pergamon 1974
- Published: January 1, 1974
- Imprint: Pergamon
- eBook ISBN: 9781483187228

## About the Authors

### L D Landau

#### Affiliations and Expertise

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