[Course of Theoretical Physics 03] • Quantum Mechanics by Landau, L.D. -- Read -- Imperial Library of Trantor

Index

Cover image Title page Table of Contents Other titles in the COURSE OF THEORETICAL PHYSICS by LANDAU and LIFSHITZ Copyright FROM THE PREFACE TO THE FIRST ENGLISH EDITION PREFACE TO THE SECOND ENGLISH EDITION PREFACE TO THE THIRD RUSSIAN EDITION EDITOR’S PREFACE TO THE FOURTH RUSSIAN EDITION NOTATION Chapter 1: THE BASIC CONCEPTS OF QUANTUM MECHANICS

§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

§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: SCHRODINGER’S EQUATION

§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

§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

§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

§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

Chapter 8: SPIN

§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

Chapter 10: THE ATOM

§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

§78 Electron terms in the diatomic molecule Solution. §79 The intersection of electron terms §80 The relation between molecular and atomic terms PROBLEMS §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

§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

Chapter 13: POLYATOMIC MOLECULES

Chapter 14: ADDITION OF ANGULAR MOMENTA

§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

§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

§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

§123 The general theory of scattering §124 An investigation of the general formula §125 The unitarity 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 §140 Scattering with spin—orbit interaction §141 Regge poles

Chapter 18: INELASTIC COLLISIONS

MATHEMATICAL APPENDICES INDEX