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Quantum Mechanics

Index of terms

Every titled definition, theorem, recipe and key idea in the book, alphabetically. Click a name to open it here, or the section number to go to it.

Essential vocabulary

Only these are flagged essential: everything else is built from them.

  1. Commutator Definition 2.3.1, §2.3
  2. Complex conjugate and modulus Definition 1.1.2, §1.1
  3. Eigenvalue and eigenfunction Definition 1.3.3, §1.3
  4. Expectation value Definition 2.2.5, §2.2
  5. Hamiltonian Definition 2.4.4, §2.4
  6. Hermitian operator Definition 1.4.1, §1.4
  7. Pauli exclusion principle Theorem 5.1.5, §5.1
  8. Pauli matrices Definition 4.1.3, §4.1
  9. State Definition 2.2.1, §2.2

Every definition, theorem and recipe

  1. Allowed and forbidden regions Definition 3.1.1, §3.1
  2. Allowed states of two particles Recipe 5.1.4, §5.1
  3. An operator from its eigenstates Recipe 4.1.1, §4.1
  4. Angular momentum Definition 4.2.1, §4.2
  5. Angular momentum matrices Recipe 4.2.4, §4.2
  6. Annihilation and creation operators Definition 3.5.4, §3.5
  7. Bandwidth Theorem 1.2.10, §1.2
  8. Bending back, bending away Key observation 3.1.3, §3.1
  9. Between the two forms Recipe 1.1.8, §1.1
  10. Bound states of the finite well Theorem 3.3.1, §3.3
  11. Bra, ket, bracket Definition 1.4.6, §1.4
  12. Building coupled states by lowering Recipe 4.4.2, §4.4
  13. Clebsch–Gordan coefficients Definition 4.4.4, §4.4
  14. Common eigenstates commute Theorem 2.3.2, §2.3
  15. Commutator Definition 2.3.1, §2.3
  16. Commutators of the ladder operators Theorem 3.5.6, §3.5
  17. Completeness Theorem 1.4.7, §1.4
  18. Complex amplitude Definition 1.2.7, §1.2
  19. Complex conjugate and modulus Definition 1.1.2, §1.1
  20. Complex number Definition 1.1.1, §1.1
  21. Components in a basis Recipe 1.4.5, §1.4
  22. Computing a commutator Recipe 2.3.3, §2.3
  23. Continuum normalisation Key observation 1.5.6, §1.5
  24. Coupling ℓ with s = ½ Theorem 4.4.6, §4.4
  25. De Broglie and Planck relations Definition 2.4.1, §2.4
  26. Dirac delta Definition 1.5.4, §1.5
  27. Eigenfunctions of momentum Theorem 1.3.8, §1.3
  28. Eigenvalue and eigenfunction Definition 1.3.3, §1.3
  29. Eigenvalues of angular momentum Theorem 4.2.2, §4.2
  30. Eigenvalues, eigenvectors, diagonal form Recipe 1.3.6, §1.3
  31. Energies of the harmonic oscillator Theorem 3.5.1, §3.5
  32. Equally spaced, never zero Key observation 3.5.2, §3.5
  33. Euler’s identity Theorem 1.1.6, §1.1
  34. Exchange operator Definition 5.1.1, §5.1
  35. Expanding in momentum eigenstates Recipe 1.5.3, §1.5
  36. Expectation value Definition 2.2.5, §2.2
  37. Expected value and spread Definition 2.1.3, §2.1
  38. Fermions and bosons Key observation 5.1.3, §5.1
  39. Forward and backward waves Theorem 1.2.2, §1.2
  40. Hamiltonian Definition 2.4.4, §2.4
  41. Harmonic plane wave Definition 1.2.3, §1.2
  42. Heisenberg’s uncertainty principle Theorem 2.5.1, §2.5
  43. Hermitian adjoint Definition 1.4.8, §1.4
  44. Hermitian operator Definition 1.4.1, §1.4
  45. How many bound states Key observation 3.3.2, §3.3
  46. How much gets through Key observation 3.4.4, §3.4
  47. Independent-electron approximation Theorem 5.2.1, §5.2
  48. Ladder operators Definition 4.2.3, §4.2
  49. Linear operator Definition 1.3.2, §1.3
  50. Measurement disturbs Key observation 2.1.1, §2.1
  51. Momentum in a box Theorem 1.5.1, §1.5
  52. Momentum is Hermitian Theorem 1.4.10, §1.4
  53. No state points along an axis Theorem 4.2.6, §4.2
  54. Normalising a Gaussian Recipe 2.5.2, §2.5
  55. Normalising a state Recipe 2.2.2, §2.2
  56. Number operator Definition 3.5.5, §3.5
  57. Operator Definition 1.3.1, §1.3
  58. Orbital commutators Theorem 4.3.1, §4.3
  59. Orthonormal basis Definition 1.4.4, §1.4
  60. Para and ortho states Theorem 5.2.2, §5.2
  61. Pauli exclusion principle Theorem 5.1.5, §5.1
  62. Pauli matrices Definition 4.1.3, §4.1
  63. Periodicity quantises m Theorem 4.3.3, §4.3
  64. Phase Definition 1.1.5, §1.1
  65. Polar form Key observation 1.1.7, §1.1
  66. Position and momentum do not commute Theorem 2.4.3, §2.4
  67. Postulate 1 Theorem 2.2.4, §2.2
  68. Probability density Definition 2.1.5, §2.1
  69. Probability distribution Definition 2.1.2, §2.1
  70. Product and coupled bases Definition 4.4.1, §4.4
  71. Products in polar form Proposition 1.1.10, §1.1
  72. Properties of a Hermitian operator Theorem 1.4.2, §1.4
  73. Properties of the delta Theorem 1.5.5, §1.5
  74. Raising and lowering operators Definition 4.1.6, §4.1
  75. Reading a harmonic wave Recipe 1.2.4, §1.2
  76. Real and imaginary part from and Proposition 1.1.4, §1.1
  77. Reflection and transmission Definition 3.4.1, §3.4
  78. Rules of addition Key observation 4.4.5, §4.4
  79. Setting up a problem Recipe 2.4.6, §2.4
  80. Solving a piecewise-constant potential Recipe 3.1.2, §3.1
  81. Solving the barrier Recipe 3.4.2, §3.4
  82. Spherical harmonics Definition 4.3.4, §4.3
  83. Spherical wave Definition 1.2.12, §1.2
  84. Spin commutators Theorem 4.1.5, §4.1
  85. State Definition 2.2.1, §2.2
  86. Stationary states Key observation 2.4.8, §2.4
  87. Symmetric and antisymmetric states Theorem 5.1.2, §5.1
  88. The cone Key observation 2.2.8, §2.2
  89. The dot product of two functions Key observation 1.4.3, §1.4
  90. The expectation value is the average result Theorem 2.2.6, §2.2
  91. The Gaussian packet’s momentum Theorem 2.5.3, §2.5
  92. The ground state Theorem 3.5.8, §3.5
  93. The infinite well Theorem 3.2.1, §3.2
  94. The ladder Theorem 3.5.7, §3.5
  95. The minimum-uncertainty state Key observation 2.5.4, §2.5
  96. The modulus from the conjugate Proposition 1.1.3, §1.1
  97. The operators in spherical coordinates Theorem 4.3.2, §4.3
  98. The rigid rotator Theorem 4.3.5, §4.3
  99. The spin-½ operators Theorem 4.1.2, §4.1
  100. The vector model Key observation 4.2.5, §4.2
  101. The wave must fit Key observation 3.2.2, §3.2
  102. Time-dependent Schrödinger equation Theorem 2.4.7, §2.4
  103. Time-independent Schrödinger equation Theorem 2.4.5, §2.4
  104. Transmission amplitude below the barrier Theorem 3.4.3, §3.4
  105. Triplet and singlet Theorem 4.4.3, §4.4
  106. Wave equation Definition 1.2.1, §1.2
  107. Wave packet Definition 1.2.9, §1.2
  108. Wavevector Definition 1.2.6, §1.2
  109. Why ortho lies below para Key observation 5.2.3, §5.2