Wave Mechanics

Foreward by Victor F. Weisskopf Preface by the Editor Preface by the Students Introduction 1. Wave Functions of Force-Free Particles 1. Association of waves with particles 2. The wave function and wave equation 3. The uncertainty principle 4. Wave packets and the mechanics of point particles. Probability density 5. Measuring arrangements. Discussion of examples 6. Classical statistics and quantum statistics 2. Description of a Particle in a Box and in Free Space 7. One particle in a box. The equation of continuity 8. Normalization in the continuum. The Dirac d-function 9. The completeness relation. Expansion theorem 10. Initial-value problem and the fundamental solution 3. Particle in a Field of Force 11. The Hamiltonian operator 12. Hermitian operators 13. Expectation values and the classical equation of motion. Commutation relations (commutators) 4. More than One Particle 14. More than one particle 5. Eigenvalue Problems. Functions of Mathematical Physics 15. The linear harmonic oscillator. Hermite polynomials 16. Matrix calculus illustrated with the linear harmonic oscillator 17. The harmonic oscillator in a plane. Degeneracy 18. The hydrogen atom 6. Collision Processes 19. Asymptotic solution of the scattering problem 20. The scattering cross section. The Rutherford scattering formula 21. Solution of the force-free wave equation 22. Expansion of a plane wave in Legendre polynomials 23. Solution of the Schrödinger equation with an arbitrary central potential 24. The Born approximation 25. Scattering of low-energy particles 7. Approximate Methods for Solving the Wave Equation 26. Eigenvalue problem of a particle in a uniform field 27. The WKB method 8. Matrices and Operators. Perturbation Theory 28. General relationship between matrices and operators. Transformation theory 29. General formalism of perturbation theory in the matrix representation 30. Time-dependent perturbation 9. Angular Momentum and Spin 31. General commutation relations 32. Matrix elements of the angular momentum 33. Spin 34. Spinors and space rotations 10. Identical Particles with Spin 35. Symmetry classes 36. The exclusion principle 37. The helium atom 38. Collision of two identical particles: Mott's theory 39. The statistics of nuclear spins Exercises 40. Fundamental solution for interval 41. Bound states and tunnel effect 42. Kronig-Penney potential 43. Spherical harmonics 44. Fundamental solution for harmonic oscillator 45. Angular momentum 46 Partial waves 47. The symmetrical top Bibliography "Appendix, Comments by the Editor" Index