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# Lectures on Quantum Mechanics for Mathematics Students

### About this Title

**L. D. Faddeev**, *Steklov Mathematical Institute, St. Petersburg, Russia* and **O. A. Yakubovski&ibreve;**, *St. Petersburg University, St. Petersburg, Russia*. Translated by **Harold H McFaden**

Publication: The Student Mathematical Library

Publication Year
2009: Volume 47

ISBNs: 978-0-8218-4699-5 (print); 978-1-4704-1633-1 (online)

DOI: http://dx.doi.org/10.1090/stml/047

MathSciNet review: MR2492178

MSC: Primary 81-01; Secondary 81Q10, 81R05, 81S30

### Table of Contents

**Front/Back Matter**

**Chapters**

- 1. The algebra of observables in classical mechanics
- 2. States
- 3. Liouville’s theorem, and two pictures of motion in classical mechanics
- 4. Physical bases of quantum mechanics
- 5. A finite-dimensional model of quantum mechanics
- 6. States in quantum mechanics
- 7. Heisenberg uncertainty relations
- 8. Physical meaning of the eigenvalues and eigenvectors of observables
- 9. Two pictures of motion in quantum mechanics. The Schrödinger equation. Stationary states
- 10. Quantum mechanics of real systems. The Heisenberg commutation relations
- 11. Coordinate and momentum representations
- 12. “Eigenfunctions” of the operators $Q$ and $P$
- 13. The energy, the angular momentum, and other examples of observables
- 14. The interconnection between quantum and classical mechanics. Passage to the limit from quantum mechanics to classical mechanics
- 15. One-dimensional problems of quantum mechanics. A free one-dimensional particle
- 16. The harmonic oscillator
- 17. The problem of the oscillator in the coordinate representation
- 18. Representation of the states of a one-dimensional particle in the sequence space $l_2$
- 19. Representation of the states for a one-dimensional particle in the space $\mathcal {D}$ of entire analytic functions
- 20. The general case of one-dimensional motion
- 21. Three-dimensional problems in quantum mechanics. A three-dimensional free particle
- 22. A three-dimensional particle in a potential field
- 23. Angular momentum
- 24. The rotation group
- 25. Representations of the rotation group
- 26. Spherically symmetric operators
- 27. Representation of rotations by $2\times 2$ unitary matrices
- 28. Representation of the rotation group on a space of entire analytic functions of two complex variables
- 29. Uniqueness of the representations $D_j$
- 30. Representations of the rotation group on the space $L^2(S^2)$. Spherical functions
- 31. The radial Schrödinger equation
- 32. The hydrogen atom. The alkali metal atoms
- 33. Perturbation theory
- 34. The variational principle
- 35. Scattering theory. Physical formulation of the problem
- 36. Scattering of a one-dimensional particle by a potential barrier
- 37. Physical meaning of the solutions $\psi _1$ and $\psi _2$
- 38. Scattering by a rectangular barrier
- 39. Scattering by a potential center
- 40. Motion of wave packets in a central force field
- 41. The integral equation of scattering theory
- 42. Derivation of a formula for the cross-section
- 43. Abstract scattering theory
- 44. Properties of commuting operators
- 45. Representation of the state space with respect to a complete set of observables
- 46. Spin
- 47. Spin of a system of two electrons
- 48. Systems of many particles. The identity principle
- 49. Symmetry of the coordinate wave functions of a system of two electrons. The helium atom
- 50. Multi-electron atoms. One-electron approximation
- 51. The self-consistent field equations
- 52. Mendeleev’s periodic system of the elements
- 53. Appendix. Lagrangian formulation of classical mechanics