Principles of Quantum Mechanics


Principles of Quantum Mechanics is a textbook by Ramamurti Shankar. The book has been through two editions. It is used in many college courses around the world.

Contents

  1. Mathematical Introduction
  2. # Linear Vector Spaces: Basics
  3. # Inner Product Spaces
  4. # Dual Spaces and the Dirac Notation
  5. # Subspaces
  6. # Linear Operators
  7. # Matrix Elements of Linear Operators
  8. # Active and Passive Transformations
  9. # The Eigenvalue Problem
  10. # Functions of Operators and Related Concepts
  11. # Generalization to Infinite Dimensions
  12. Review of Classical Mechanics
  13. # The Principle of Least Action and Lagrangian Mechanics
  14. # The Electromagnetic Lagrangian
  15. # The Two-Body Problem
  16. # How Smart Is a Particle?
  17. # The Hamiltonian Formalism
  18. # The Electromagnetic Force in the Hamiltonian Scheme
  19. # Cyclic Coordinates, Poisson Brackets, and Canonical Transformations
  20. # Symmetries and Their Consequences
  21. All Is Not Well with Classical Mechanics
  22. # Particles and Waves in Classical Physics
  23. # An Experiment with Waves and Particles
  24. # The Double-Slit Experiment with Light
  25. # Matter Waves (de Broglie Waves)
  26. # Conclusions
  27. The Postulates – a General Discussion
  28. #The Postulates
  29. #Discussion of Postulates I-III
  30. #The Schrödinger Equation
  31. Simple Problems in One Dimension
  32. # The Free Particle
  33. # The Particle in a Box
  34. # The Continuity Equation for Probability
  35. # The Single-Step Potential: a Problem in Scattering
  36. # The Double-Slit Experiment
  37. # Some Theorems
  38. The Classical Limit
  39. The Harmonic Oscillator
  40. # Why Study the Harmonic Oscillator?
  41. # Review of the Classical Oscillator
  42. # Quantization of the Oscillator
  43. # The Oscillator in the Energy Basis
  44. # Passage from the Energy Basis to the Basis
  45. The Path Integral Formulation of Quantum Theory
  46. # The Path Integral Recipe
  47. # Analysis of the Recipe
  48. # An Approximation to for the Free Particle
  49. # Path Integral Evaluation of the Free-Particle Propagator
  50. # Equivalence to the Schrodinger Equation
  51. # Potentials of the Form
  52. The Heisenberg Uncertainty Relations
  53. # Introduction
  54. # Derivation of the Uncertainty Relations
  55. # The Minimum Uncertainty Packet
  56. # Applications of the Uncertainty Principle
  57. # The Energy-Time Uncertainty Relation
  58. Systems with Degrees of Freedom
  59. # Particles in One Dimension
  60. # More Particles in More Dimensions
  61. # Identical Particles
  62. Symmetries and Their Consequences
  63. # Overview
  64. # Translational Invariance in Quantum Theory
  65. # Time Translational In variance
  66. # Parity Invariance
  67. # Time-Reversal Symmetry
  68. Rotational Invariance and Angular Momentum
  69. # Translations in Two Dimensions
  70. # Rotations in Two Dimensions
  71. # The Eigenvalue Problem of
  72. # Angular Momentum in Three Dimensions
  73. # The Eigenvalue Problem of and
  74. # Solution of Rotationally Invariant Problems
  75. The Hydrogen Atom
  76. # The Eigenvalue Problem
  77. # The Degeneracy of the Hydrogen Spectrum
  78. # Numerical Estimates and Comparison with Experiment
  79. # Multielectron Atoms and the Periodic Table
  80. Spin
  81. #Introduction
  82. #What is the Nature of Spin?
  83. #Kinematics of Spin
  84. #Spin Dynamics
  85. #Return of Orbital Degrees of Freedom
  86. Addition of Angular Momenta
  87. # A Simple Example
  88. # The General Problem
  89. # Irreducible Tensor Operators
  90. # Explanation of Some "Accidental" Degeneracies
  91. Variational and WKB Methods
  92. #The Variational Method
  93. #The Wentzel-Kramers-Brillouin Method
  94. Time-Independent Perturbation Theory
  95. # The Formalism
  96. # Some Examples
  97. # Degenerate Perturbation Theory
  98. Time-Dependent Perturbation Theory
  99. # The Problem
  100. # First-Order Perturbation Theory
  101. # Higher Orders in Perturbation Theory
  102. # A General Discussion of Electromagnetic Interactions
  103. # Interaction of Atoms with Electromagnetic Radiation
  104. Scattering Theory
  105. # Introduction
  106. # Recapitulation of One-Dimensional Scattering and Overview
  107. # The Born Approximation
  108. # Born Again
  109. # The Partial Wave Expansion
  110. # Two-Particle Scattering
  111. The Dirac Equation
  112. # The Free-Particle Dirac Equation
  113. # Electromagnetic Interaction of the Dirac Particle
  114. # More on Relativistic Quantum Mechanics
  115. Path Integrals – II
  116. # Derivation of the Path Integral
  117. # Imaginary Time Formalism
  118. # Spin and Fermion Path Integrals
  119. # Summary
  120. Appendix
  121. # Matrix Inversion
  122. # Gaussian Integrals
  123. # Complex Numbers
  124. # The Prescription

Reviews

Physics Bulletin said about the book, "No matter how gently one introduces students to the concept of Dirac’s bras and kets, many are turned off. Shankar attacks the problem head-on in the first chapter, and in a very informal style suggests that there is nothing to be frightened of". American Scientist called it "An excellent text … The postulates of quantum mechanics and the mathematical underpinnings are discussed in a clear, succinct manner".