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 (Classical)
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 (Dotting Your 's and Crossing your 's)
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 (Coordinate Basis)
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 (Time-Dependent Description)
108. Born Again (The Time-Independent Approximation)
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