Introduction to Quantum Mechanics

by Delmar Larsen

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This text focuses on introducing students to the postulates and general principles of quantum mechanics. Application to harmonic oscillator, rigid rotor, one-electron and many-electron atoms, and homo- and hetero-nuclear diatomic molecules are discussed including variational method and time-independent perturbation theory approximations.

Description from LibreTexts.

Publisher
University of California, Davis
Subjects
Chemistry
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

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  1. Front Matter
  2. TitlePage
  3. InfoPage
  4. Table of Contents
  5. Licensing
  6. 1: The Dawn of the Quantum Theory
  7. 1.1: Blackbody Radiation Cannot Be Explained Classically
  8. 1.2: Quantum Hypothesis used for Blackbody Radiation Law
  9. 1.3: Photoelectric Effect Explained with Quantum Hypothesis
  10. 1.4: The Hydrogen Atomic Spectrum
  11. 1.5: The Rydberg Formula and the Hydrogen Atomic Spectrum
  12. 1.6: Matter Has Wavelike Properties
  13. 1.7: de Broglie Waves can be Experimentally Observed
  14. 1.8: The Bohr Theory of the Hydrogen Atom
  15. 1.9: The Heisenberg Uncertainty Principle
  16. 1.E: The Dawn of the Quantum Theory (Exercises)
  17. 2: The Classical Wave Equation
  18. 2.1: The One-Dimensional Wave Equation
  19. 2.2: The Method of Separation of Variables
  20. 2.3: Oscillatory Solutions to Differential Equations
  21. 2.4: The General Solution is a Superposition of Normal Modes
  22. 2.5: A Vibrating Membrane
  23. 2.E: The Classical Wave Equation (Exercises)
  24. 3: The Schrödinger Equation & a Particle in a Box
  25. 3.1: The Schrödinger Equation
  26. 3.2: Linear Operators in Quantum Mechanics
  27. 3.3: The Schrödinger Equation is an Eigenvalue Problem
  28. 3.4: The Quantum Mechanical Free Particle
  29. 3.5: Wavefunctions Have a Probabilistic Interpretation
  30. 3.6: The Energy of a Particle in a Box is Quantized
  31. 3.7: Wavefunctions Must Be Normalized
  32. 3.8: The Average Momentum of a Particle in a Box is Zero
  33. 3.9B: Particle in a Finite Box and Tunneling (optional)
  34. 3.9: The Uncertainty Principle Redux - Estimating Uncertainties from Wavefunctions
  35. 3.10: A Particle in a Two-Dimensional Box
  36. 3.11: A Particle in a Three-Dimensional Box
  37. 3.E: The Schrödinger Equation and a Particle in a Box (Exercises)
  38. 4: Postulates and Principles of Quantum Mechanics
  39. 4.1: The Wavefunction Specifies the State of a System
  40. 4.2: Quantum Operators Represent Classical Variables
  41. 4.3: Observable Quantities Must Be Eigenvalues of Quantum Mechanical Operators
  42. 4.4: The Time-Dependent Schrödinger Equation
  43. 4.5: The Eigenfunctions of Operators are Orthogonal
  44. 4.6: Heisenburg Uncertainy Principle III - Commuting Operators
  45. 4.E: Postulates and Principles of Quantum Mechanics (Exercises)
  46. 5: The Harmonic Oscillator and the Rigid Rotor
  47. 5.1: A Harmonic Oscillator Obeys Hooke's Law
  48. 5.2: The Equation for a Harmonic-Oscillator Model of a Diatomic Molecule Contains the Reduced Mass of the Molecule
  49. 5.3: The Harmonic Oscillator is an Approximation
  50. 5.4: The Harmonic Oscillator Energy Levels
  51. 5.5: The Harmonic Oscillator and Infrared Spectra
  52. 5.6: The Harmonic-Oscillator Wavefunctions Involve Hermite Polynomials
  53. 5.7: Hermite Polynomials are either Even or Odd Functions
  54. 5.8: The Energy Levels of a Rigid Rotor
  55. 5.9: The Rigid Rotator is a Model for a Rotating Diatomic Molecule
  56. 5.E: The Harmonic Oscillator and the Rigid Rotor (Exercises)
  57. 6: The Hydrogen Atom
  58. 6.1: The Schrödinger Equation for the Hydrogen Atom Can Be Solved Exactly
  59. 6.2: The Wavefunctions of a Rigid Rotator are Called Spherical Harmonics
  60. 6.3: The Three Components of Angular Momentum Cannot be Measured Simultaneously with Arbitrary Precision
  61. 6.4: Hydrogen Atomic Orbitals Depend upon Three Quantum Numbers
  62. 6.5: s Orbitals are Spherically Symmetric
  63. 6.6: Orbital Angular Momentum and the p-orbitals
  64. 6.7: The Helium Atom Cannot Be Solved Exactly
  65. 6.E: The Hydrogen Atom (Exercises)
  66. 7: Approximation Methods
  67. 7.0: Slater's Rules for Shielding
  68. 7.1: The Variational Method
  69. 7.2: Linear Variational Method and the Secular Determinant
  70. 7.3: Trial Functions Can Be Linear Combinations of Functions with Variational Parameters
  71. 7.4: Perturbation Theory Expresses the Solutions in Terms of Solved Problems
  72. 7.E: Approximation Methods (Exercises)
  73. 8: Multielectron Atoms
  74. 8.1: Atomic and Molecular Calculations are Expressed in Atomic Units
  75. 8.2: Perturbation Theory and the Variational Method for Helium
  76. 8.3: Hartree-Fock Equations are Solved by the Self-Consistent Field Method
  77. 8.4: An Electron Has An Intrinsic Spin Angular Momentum
  78. 8.5: Wavefunctions must be Antisymmetric to Interchange of any Two Electrons
  79. 8.6: Antisymmetric Wave Functions can be Represented by Slater Determinants
  80. 8.7: Hartree-Fock Calculations Give Good Agreement with Experimental Data
  81. 8.8: Term Symbols Gives Detailed Descriptions of an Electron Configuration
  82. 8.8B: Multi-electron Considerations - A Closer Look at Helium
  83. 8.9: The Allowed Values of J - the Total Angular Momentum Quantum Number
  84. 8.10: Hund's Rules Determine the Term Symbols of the Ground Electronic States
  85. 8.11: Using Atomic Term Symbols to Describe Atomic Spectra
  86. 8.E: Multielectron Atoms (Exercises)
  87. 9: The Chemical Bond: Diatomic Molecules
  88. 9.1: The Born-Oppenheimer Approximation Simplifies the Molecular Schrödinger Equation
  89. 9.2: The H₂⁺ Prototypical Species
  90. 9.2B: Solving the H₂⁺ System Exactly (Optional)
  91. 9.3: The Overlap Integral
  92. 9.3B: Evaluating the Overlap Integral (Optional)
  93. 9.4: Chemical Bond Stability
  94. 9.5: Bonding and Antibonding Orbitals
  95. 9.6: A Simple Molecular-Orbital Treatment of H₂ Places Both Electrons in a Bonding Orbital
  96. 9.7: Molecular Orbitals Can Be Ordered According to Their Energies
  97. 9.8: Molecular-Orbital Theory Does not Predict a Stable Diatomic Helium Molecule
  98. 9.9: Electrons Populate Molecular Orbitals According to the Pauli Exclusion Principle
  99. 9.10: Molecular Orbital Theory Predicts that Molecular Oxygen is Paramagnetic
  100. 9.E: The Chemical Bond: Diatomic Molecules (Exercises)
  101. MathChapters
  102. A: Complex Numbers
  103. B: Probability and Statistics
  104. C: Vectors
  105. D: Spherical Coordinates
  106. E: Determinants
  107. F: Matrices
  108. G: Numerical Methods
  109. H: Partial Differentiation
  110. I: Series and Limits
  111. J: The Binomial Distribution and Stirling's Appromixation
  112. Back Matter
  113. Index
  114. Glossary
  115. Detailed Licensing