Quantum Mechanics

by Niels Walet

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Publisher
University of Manchester
Subjects
Physics, Quantum Mechanics
Licence
CC BY-NC-SA 2.0, as LibreTexts states it. Non-commercial use only.
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Tweens profiles and older, judged from its title and subjects

Contents

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  1. Front Matter
  2. TitlePage
  3. InfoPage
  4. Table of Contents
  5. Licensing
  6. 1: Introduction to Quantum Mechanics
  7. 1.1: Black-body radiation
  8. 1.2: Photo-electric effect
  9. 1.3: Hydrogen Atom
  10. 1.4: Wave particle duality
  11. 1.5: Uncertainty
  12. 1.6: Tunneling
  13. 2: Concepts from Classical Mechanics
  14. 2.1: Conservative Fields
  15. 2.2: Energy Function
  16. 2.3: Simple Example
  17. 3: The Schrödinger Equation
  18. 3.1: The State of a Quantum System
  19. 3.2: Operators
  20. 3.3: Analysis of the wave equation
  21. 4: Bound states of the Square Well
  22. 4.1: Bound States
  23. 4.2: B₂= 0
  24. 4.3: A₂= 0
  25. 4.4: Some Consequences
  26. 4.5: Lessons from the square well
  27. 4.6: A physical system (approximately) described by a square well
  28. 5: Infinite Wells
  29. 5.1: Zero of Energy is Arbitrary
  30. 5.2: Solution
  31. 6: Scattering from Potential Steps and Square Barriers
  32. 6.1: Non-normalizable Wavefunctions
  33. 6.2: Potential step
  34. 6.3: Square Barrier
  35. 7: The Harmonic Oscillator
  36. 7.1: Prelude to Harmonic Oscillators
  37. 7.2: Dimensionless Coordinates
  38. 7.3: Behaviour for large |y|
  39. 7.4: Taylor Series Solution
  40. 7.5: A Few Solutions
  41. 7.6: Quantum-Classical Correspondence
  42. 8: The Formalism Underlying Quantum Mechanics
  43. 8.1: Key Postulates
  44. 8.2: Expectation Values of x² and p² for the Harmonic Oscillator
  45. 8.3: The Measurement Process
  46. 9: Ladder operators
  47. 9.1: Harmonic oscillators
  48. 9.2: The operators  and †.
  49. 9.3: Eigenfunctions of H through ladder operations
  50. 9.4: Normalisation and Hermitean conjugates
  51. 10: Time-Dependent Wavefunctions
  52. 10.1: Correspondence between time-dependent and time-independent solutions
  53. 10.2: Superposition of time-dependent solutions
  54. 10.3: Completeness and time-dependence
  55. 10.4: Simple Example
  56. 10.5: Wave packets (states of minimal uncertainty)
  57. 11: 3D Schrödinger Equation
  58. 11.1: The momentum operator as a vector
  59. 11.2: Spherical Coordinates
  60. 11.3: Solutions independent of angular variables
  61. 11.4: The hydrogen atom
  62. 11.5: Now where does the probability peak?
  63. 11.6: Spherical Harmonics
  64. 11.7: General solutions
  65. 12: Quantum Mechanics of the Hydrogen Atom
  66. 12.1: The Uncertainty Principle
  67. 12.2: Bohr Model of the Hydrogen Atom
  68. 12.3: Schrödinger Theory of the Hydrogen Atom
  69. 12.3.1: Schrödinger Theory of Hydrogen
  70. 12.3.2: The Spin-Orbit Effect
  71. 12.3.3: Kinetic Energy Corrections
  72. 12.4: Dirac Theory of the Hydrogen Atom
  73. 12.5: Smaller Effects
  74. 12.5.1: Hyperfine Structure
  75. 12.5.2: The Lamb Shift
  76. 12.5.3: The Zeeman Effect
  77. 12.6: Conclusion and References
  78. 13: Miscellaneous Quantum Mechanics Topics
  79. 13.1: Bell's Theorem
  80. 13.2: Black Hole Thermodynamics
  81. 13.3: Complementarity and Copenhagen Interpretation
  82. 13.4: Double Slit
  83. 13.5: Flash Animations for Physics
  84. 13.6: Locality and Quantum Mechanics
  85. 13.7: Particle in a 2-dimensional box
  86. 13.8: Quantum Entanglement
  87. 13.9: Quantum Interference
  88. 13.10: Quantum Mechanics- a Poor Person's Guide
  89. 13.11: Quantum Mechanics- Interpretation
  90. 13.12: Quantum Teleportation
  91. 13.13: Schrödinger's Cat
  92. 13.14: Stern-Gerlach Experiment
  93. 13.15: The Bohr Model of the Atom
  94. 13.16: The Development of Quantum Mechanics
  95. 13.17: Two analogies to Bell's Theorem
  96. 13.18: Wave-Particle Duality
  97. Back Matter
  98. Index
  99. Detailed Licensing