vi Contents

§14. The interconnection between quantum and classical

mechanics. Passage to the limit from quantum

mechanics to classical mechanics 69

§15. One-dimensional problems of quantum mechanics. A

free one-dimensional particle 77

§16. The harmonic oscillator 83

§17. The problem of the oscillator in the coordinate

representation 87

§18. Representation of the states of a one-dimensional

particle in the sequence space l2 90

§19. Representation of the states for a one-dimensional

particle in the space D of entire analytic functions 94

§20. The general case of one-dimensional motion 95

§21. Three-dimensional problems in quantum mechanics. A

three-dimensional free particle 103

§22. A three-dimensional particle in a potential field 104

§23. Angular momentum 106

§24. The rotation group 108

§25. Representations of the rotation group 111

§26. Spherically symmetric operators 114

§27. Representation of rotations by 2 × 2 unitary matrices 117

§28. Representation of the rotation group on a space of entire

analytic functions of two complex variables 120

§29. Uniqueness of the representations Dj 123

§30. Representations of the rotation group on the space

L2(S2).

Spherical functions 127

§31. The radial Schr¨ odinger equation 130

§32. The hydrogen atom. The alkali metal atoms 136

§33. Perturbation theory 147

§34. The variational principle 154

§35. Scattering theory. Physical formulation of the problem 157

§36. Scattering of a one-dimensional particle by a potential

barrier 159