Introductory Quantum Mechanics

by Richard Fitzpatrick

Read here Read at LibreTextsPDF

This book is intendedas an introductory course on non-relativistic quantum mechanics. Readers need to be reasonably familiar with Newtonian dynamics, elementary classical electromagnetism and special relativity, the physics and mathematics of waves (including the representation of waves via complex functions), basic probability theory, ordinary and partial differential equations, linear algebra, vector algebra, and Fourier series and transforms.

Description from LibreTexts.

Publisher
University of Texas at Austin
Subjects
Physics, Quantum Mechanics
Licence
CC BY-NC-SA 4.0, as LibreTexts states it. Non-commercial use only.
Who can read
Tweens profiles and older, judged from its title and subjects

Contents

LibreTexts writes equations in TeX, and here they show as TeX; the PDF has them typeset.

  1. Front Matter
  2. TitlePage
  3. InfoPage
  4. Table of Contents
  5. Licensing
  6. Preface
  7. 1: Probability Theory
  8. 1.1: What is Probability?
  9. 1.2: Combining Probabilities
  10. 1.3: Mean, Variance, and Standard Deviation
  11. 1.4: Continuous Probability Distributions
  12. 1.5: Exercises
  13. 2: Wave-Particle Duality
  14. 2.1: Wavefunctions
  15. 2.2: Plane-Waves
  16. 2.3: Representation of Waves via Complex Functions
  17. 2.4: Classical Light-Waves
  18. 2.5: Photoelectric Effect
  19. 2.6: Quantum Theory of Light
  20. 2.7: Classical Interferences of Light Waves
  21. 2.8: Quantum Interference of Light
  22. 2.9: Particles
  23. 2.10: Wave-Packets
  24. 2.11: Evolution of Wave-Packets
  25. 2.12: Heisenberg’s Uncertainty Principle
  26. 2.13: Schrodinger's Equation and Wavefunction Collapse
  27. 2.14: Exercises
  28. 3: Fundamentals of Quantum Mechanics
  29. 3.1: Schrödinger's Equation
  30. 3.2: Normalization of the Wavefunction
  31. 3.3: Expectation Values (Averages) and Variances
  32. 3.4: Ehrenfest's Theorem
  33. 3.5: Operators
  34. 3.6: Momentum Representation
  35. 3.7: Heisenberg's Uncertainty Principle
  36. 3.8: Eigenstates and Eigenvalues
  37. 3.9: Measurement
  38. 3.10: Continuous Eigenvalues
  39. 3.11: Stationary States
  40. 3.12: Exercises
  41. 4: One-Dimensional Potentials
  42. 4.1: Infinite Potential Well
  43. 4.2: Square Potential Barrier
  44. 4.3: WKB Approximation
  45. 4.4: Cold Emission
  46. 4.5: Alpha Decay
  47. 4.6: Square Potential Well
  48. 4.7: Simple Harmonic Oscillator
  49. 4.E: One-Dimensional Potentials (Exercises)
  50. 5: Multi-Particle Systems
  51. 5.1: Fundamental Concepts of Multi-Particle Systems
  52. 5.2: Non-interacting Particles
  53. 5.3: Two-Particle Systems
  54. 5.4: Identical Particles
  55. 5.E: Multi-Particle Systems (Exercises)
  56. 6: Three-Dimensional Quantum Mechanics
  57. 6.1: Fundamental Concepts
  58. 6.2: Particle in Box
  59. 6.3: Degenerate Electron Gases
  60. 6.4: White Dwarf Stars
  61. 6.5: Exercises
  62. 7: Orbital Angular Momentum
  63. 7.1: Angular Momenum Operators
  64. 7.2: Representation of Angular Momentum
  65. 7.3: Eigenstates of Angular Momentum
  66. 7.4: Eigenvalues of Lz
  67. 7.5: Eigenvalues of L²
  68. 7.6: Spherical Harmonics
  69. 7.E: Orbital Angular Momentum (Exercises)
  70. 8: Central Potentials
  71. 8.1: Derivation of Radial Equation
  72. 8.2: Infinite Spherical Potential Well
  73. 8.3: Hydrogen Atom
  74. 8.4: Rydberg Formula
  75. 8.E: Central Potentials (Exercises)
  76. 9: Spin Angular Momentum
  77. 9.1: Spin Operators
  78. 9.2: Spin Space
  79. 9.3: Eigenstates of Sz and S²
  80. 9.4: Pauli Representation
  81. 9.5: Spin Precession
  82. 9.E: Spin Angular Momentum (Exercises)
  83. 10: Addition of Angular Momentum
  84. 10.1: General Principles of Angular Momentum
  85. 10.2: Angular Momentum in Hydrogen Atom
  86. 10.3: Two Spin One-Half Particles
  87. 10.E: Addition of Angular Momentum (Exercises)
  88. 11: Time-Independent Perturbation Theory
  89. 11.1: Improved Notation
  90. 11.2: Two-State System
  91. 11.3: Non-Degenerate Perturbation Theory
  92. 11.4: Quadratic Stark Effect
  93. 11.5: Degenerate Perturbation Theory
  94. 11.6: Linear Stark Effect
  95. 11.7: Fine Structure of Hydrogen
  96. 11.8: Zeeman Effect
  97. 11.9: Hyperfine Structure
  98. 11.10: Exercises
  99. 12: Time-Dependent Perturbation Theory
  100. 12.1: Preliminary Analysis
  101. 12.2: Two-State System
  102. 12.3: Spin Magnetic Resonance
  103. 12.4: Perturbation Expansion
  104. 12.5: Harmonic Perturbation
  105. 12.6: Electromagnetic Radiation
  106. 12.7: Electric Dipole Approximation
  107. 12.8: Spontaneous Emission
  108. 12.9: Radiation from Harmonic Oscillator
  109. 12.10: Selection Rules (Hydrogen Atoms)
  110. 12.11: 2P→1S Transitions in Hydrogen
  111. 12.12: Intensity Rules
  112. 12.13: Forbidden Transitions
  113. 12.E: Time-Dependent Perturbation Theory (Exercises)
  114. 13: Variational Methods
  115. 13.1: Variational Principle
  116. 13.2: Helium Atom
  117. 13.3: Hydrogen Molecule Ion
  118. 13.4: Exercises
  119. 14: Scattering Theory
  120. 14.1: Fundamentals of Scattering Theory
  121. 14.2: Born Approximation
  122. 14.3: Partial Waves
  123. 14.4: Optical Theorem
  124. 14.5: Determination of Phase-Shifts
  125. 14.6: Hard-Sphere Scattering
  126. 14.7: Low-Energy Scattering
  127. 14.8: Resonances
  128. 14.9: Exercises
  129. Back Matter
  130. Index
  131. Glossary
  132. Detailed Licensing
  133. Bibliography