Practical Quantum Mechanics

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I. General Concepts.- 1. Law of probability conservation.- 2. Variational principle of Schrödinger.- 3. Classical mechanics for space averages.- 4. Classical laws for angular motion.- 5. Energy conservation law.- 6. Hermitian conjugate.- 7. Construction of an hermitian operator.- 8. Derivatives of an operator.- 9. Time rate of an expectation value.- 10. Schrödinger and Heisenberg representations.- 11. Time dependent hamiltonian.- 12. Repeated measurement.- 13. Curvilinear coordinates.- 14. Momentum space wave functions.- 15. Momentum space: Periodic and aperiodic wave functions.- II. One-Body Problems without Spin.- A. One-Dimensional Problems.- 16. Force-free case: Basic solutions.- 17. Force-free case: Wave packet.- 18. Standing wave.- 19. Opaque division wall.- 20. Opaque wall described by Dirac ? function.- 21. Scattering at a Dirac ? function wall.- 22. Scattering at a symmetric potential barrier.- 23. Reflection at a rectangular barrier.- 24. Inversion of reflection.- 25. Rectangular potential hole.- 26. Rectangular potential hole between two walls.- 27. Virtual levels.- 28. Periodic potential.- 29. Diraccomb.- 30. Harmonic oscillator.- 31. Oscillator in Hilbert space.- 32. Oscillator eigenfunctions constructed by Hilbert space operators.- 33. Harmonic oscillator in matrix notation.- 34. Momentum space wave functions of oscillator.- 35. Anharmonic oscillator.- 36. Approximate wave functions.- 37. Potential step.- 38. Pöschl-Teller potential hole.- 39. Potential hole of modified Pöschl-Teller type.- 40. Free fall of a body over earth s surface.- 41. Accelerating electrical field.- B. Problems of Two or Three Degrees of Freedom without Spherical Symmetry.- 42. Circular oscillator.- 43. Stark effect of a two-dimensional rotator.- 44. Ionized hydrogen molecule.- 45. Oblique incidence of a plane wave.- 46. Symmetrical top.- C. The Angular Momentum.- 47. Infinitesimal rotation.- 48. Components in polar coordinates.- 49. Angular momentum and Laplacian.- 50. Hilbert space transformations.- 51. Commutators in Schrödinger representation.- 52. Particlcs of spin 1.- 53. Commutation with a tensor.- 54. Quadrupole tensor. Spherical harmonics.- 55. Transformation of spherical harmonics.- 56. Construction of Hilbert space for an angular momentum component.- 57. Orthogonality of spherical harmonics.- D. Potentials of Spherical Symmetry.- a) Bound States.- 58. Angular momentum expectation values.- 59. Construction of radial momentum operator.- 60. Solutions neighbouring eigenfunctions.- 61. Quadrupole moment.- 62. Particle enclosed in a sphere.- 63. Square well of finite depth.- 64. Wood-Saxon potential.- 65. Spherical oscillator.- 66. Degeneracy of the spherical oscillator.- 67. Kepler problem.- 68. Hulthén potential.- 69. Kratzer s molecular potential.- 70. Morse potential.- 71. Rotation correction of Morse formula.- 72. Yukawa potential hole.- 73. Isotope shift in x-rays.- 74. Muonic atom ground state.- 75. Central-force model of deuteron.- 76. Momentum space wave functions for central force potentials.- 77. Momentum space integral equation for central force potentials.- 78. Momentum space wave functions for hydrogen.- 79. Stark effect of a three-dimensional rotator.- b) Problems of Elastic Scattering.- 80. Interference of incident and scattered waves.- 81. Partial wave expansion of plane wave.- 82. Partial wave expansion of scattering amplitude.- 83. Scattering at low energies.- 84. Scattering by a constant repulsive potential.- 85. Anomalous scattering.- 86. Scattering resonances.- 87. Contribution of higher angular momenta.- 88. Shape-independent approximation.- 89. Rectangular hole: Low-energy scattering.- 90. Low-energy scattering and bound state.- 91. Deuteron potential with and without hard core.- 92. Low-energy cross section with and without hard core.- 93. Low-energy scattering by a modified Pöschl-Teller potential hole.- 94. Radial integral equation.- 95. Variational principle of Schwinger.- 96. Successive approximatio