L. D. Faddeev: Steklov Mathematical Institute, St. Petersburg, Russia,
O. A. Yakubovskii: St. Petersburg University, St. Petersburg, Russia

• Preface 12
• Preface to the English edition 14
• The algebra of observables in classical mechanics 16
• States 21
• Liouville’s theorem, and two pictures of motion in classical mechanics 28
• Physical bases of quantum mechanics 30
• A finite-dimensional model of quantum mechanics 42
• States in quantum mechanics 47
• Heisenberg uncertainty relations 51
• Physical meaning of the eigenvalues and eigenvectors of observables 54
• Two pictures of motion in quantum mechanics. The Schrödinger equation. Stationary states 59
• Quantum mechanics of real systems. The Heisenberg commutation relations 64
• Coordinate and momentum representations 69
• “Eigenfunctions” of the operators Q and P 75
• The energy, the angular momentum, and other examples of observables 78
• The interconnection between quantum and classical mechanics. Passage to the limit from quantum mechanics to classical mechanics 84
• One-dimensional problems of quantum mechanics. A free one-dimensional particle 92
• The harmonic oscillator 98
• The problem of the oscillator in the coordinate representation 102
• Representation of the states of a one-dimensional particle in the sequence space l2105
• Representation of the states for a one-dimensional particle in the space D of entire analytic functions 109
• The general case of one-dimensional motion 110
• Three-dimensional problems in quantum mechanics. A three-dimensional free particle 118
• A three-dimensional particle in a potential field 119
• Angular momentum 121
• The rotation group 123
• Representations of the rotation group 126
• Spherically symmetric operators 129
• Representation of rotations by 2×2 unitary matrices 132
• Representation of the rotation group on a space of entire analytic functions of two complex variables 135
• Uniqueness of the representations Dj 138
• Representations of the rotation group on the space L²(S²) Spherical functions 142
• The radial Schrödinger equation 145
• The hydrogen atom. The alkali metal atoms 151
• Perturbation theory 162
• The variational principle 169
• Scattering theory. Physical formulation of the problem 172
• Scattering of a one-dimensional particle by a potential barrier 174
• Physical meaning of the solutions ? ₁ and ? ₂  179
• Scattering by a rectangular barrier 182
• Scattering by a potential center 184
• Motion of wave packets in a central force field 190
• The integral equation of scattering theory 196
• Derivation of a formula for the cross-section 198
• Abstract scattering theory 203
• Properties of commuting operators 212
• Representation of the state space with respect to a complete set of observables 216
• Spin 218
• Spin of a system of two electrons 223
• Systems of many particles. The identity principle 227
• Symmetry of the coordinate wave functions of a system of two electrons. The helium atom 230
• Multi-electron atoms. One-electron approximation 232
• The self-consistent field equations 238
• Mendeleev’s periodic system of the elements 241
• Lagrangian formulation of classical mechanics 246