CHEM 110A: Introduction to Quantum Mechanics

by Delmar Larsen

Read here Read at LibreTextsPDF

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

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. 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 and the Particle-in-a-Box Model
  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. 3.9: The Uncertainty Principle Redux - Estimating Uncertainties from Wavefunctions
  34. 3.10: Particle in a Finite Box and Tunneling (Optional)
  35. 3.11: A Particle in a Two-Dimensional Box
  36. 3.12: A Particle in a Three-Dimensional Box
  37. 3.E: The Schrödinger Equation and a Particle in a Box (Exercises)
  38. 3.I: Interactive Worksheets
  39. 3.I.1: Free Particle (Python Notebook)
  40. 3.I.2: Particle in an Infinite Potential Box (Python Notebook)
  41. 3.I.3: Particle in a Finite Potential Box (Python Notebook)
  42. 4: Postulates and Principles of Quantum Mechanics
  43. 4.1: The Wavefunction Specifies the State of a System
  44. 4.2: Quantum Operators Represent Classical Variables
  45. 4.3: Observable Quantities Must Be Eigenvalues of Quantum Mechanical Operators
  46. 4.4: The Time-Dependent Schrödinger Equation
  47. 4.5: The Eigenfunctions of Operators are Orthogonal
  48. 4.6: Heisenburg Uncertainy Principle III - Commuting Operators
  49. 4.E: Postulates and Principles of Quantum Mechanics (Exercises)
  50. 5: The Harmonic Oscillator and the Rigid Rotor
  51. 5.1: A Harmonic Oscillator Obeys Hooke's Law
  52. 5.2: The Equation for a Harmonic-Oscillator Model of a Diatomic Molecule Contains the Reduced Mass of the Molecule
  53. 5.3: The Harmonic Oscillator is an Approximation
  54. 5.4: The Harmonic Oscillator Energy Levels
  55. 5.5: The Harmonic Oscillator and Infrared Spectra
  56. 5.6: The Harmonic-Oscillator Wavefunctions Involve Hermite Polynomials
  57. 5.7: Hermite Polynomials are either Even or Odd Functions
  58. 5.8: The Energy Levels of a Rigid Rotor
  59. 5.9: The Rigid Rotator is a Model for a Rotating Diatomic Molecule
  60. 5.E: The Harmonic Oscillator and the Rigid Rotor (Exercises)
  61. 5.I: Interactive Worksheets
  62. 5.2I: Spherical Harmonics Visualization
  63. 5.I1: Simple Harmonic Oscillator - Plotting Eigenstates
  64. 6: The Hydrogen Atom
  65. 6.1: The Schrödinger Equation for the Hydrogen Atom Can Be Solved Exactly
  66. 6.2: The Wavefunctions of a Rigid Rotator are Called Spherical Harmonics
  67. 6.3: The Three Components of Angular Momentum Cannot be Measured Simultaneously with Arbitrary Precision
  68. 6.4: Hydrogen Atomic Orbitals Depend upon Three Quantum Numbers
  69. 6.5: s Orbitals are Spherically Symmetric
  70. 6.6: Orbital Angular Momentum and the p-orbitals
  71. 6.7: The Helium Atom Cannot Be Solved Exactly
  72. 6.E: The Hydrogen Atom (Exercises)
  73. 7: Approximation Methods
  74. 7.1: Slater's Rules for Shielding
  75. 7.2: The Variational Method
  76. 7.3: Linear Variational Method and the Secular Determinant
  77. 7.4: Trial Functions Can Be Linear Combinations of Functions with Variational Parameters
  78. 7.5: Perturbation Theory Expresses the Solutions in Terms of Solved Problems
  79. 7.E: Approximation Methods (Exercises)
  80. 8: Multielectron Atoms
  81. 8.1: Atomic and Molecular Calculations are Expressed in Atomic Units
  82. 8.2: Perturbation Theory and the Variational Method for Helium
  83. 8.3: Hartree-Fock Equations are Solved by the Self-Consistent Field Method
  84. 8.4: An Electron Has An Intrinsic Spin Angular Momentum
  85. 8.5: Wavefunctions must be Antisymmetric to Interchange of any Two Electrons
  86. 8.6: Antisymmetric Wave Functions can be Represented by Slater Determinants
  87. 8.7: Hartree-Fock Calculations Give Good Agreement with Experimental Data
  88. 8.8: Term Symbols Gives Detailed Descriptions of an Electron Configuration
  89. 8.9: Multi-electron Considerations - A Closer Look at Helium
  90. 8.10: The Allowed Values of J - the Total Angular Momentum Quantum Number
  91. 8.11: Hund's Rules Determine the Term Symbols of the Ground Electronic States
  92. 8.12: Using Atomic Term Symbols to Describe Atomic Spectra
  93. 8.E: Multielectron Atoms (Exercises)
  94. 9: The Chemical Bond- Diatomic Molecules
  95. 9.1: The Born-Oppenheimer Approximation Simplifies the Molecular Schrödinger Equation
  96. 9.2: The H₂⁺ Prototypical Species
  97. 9.3: Solving the H₂⁺ System Exactly (Optional)
  98. 9.4: The Overlap Integral
  99. 9.5: Evaluating the Overlap Integral (Optional)
  100. 9.6: Chemical Bond Stability
  101. 9.7: Bonding and Antibonding Orbitals
  102. 9.8: A Simple Molecular-Orbital Treatment of H₂ Places Both Electrons in a Bonding Orbital
  103. 9.9: Molecular Orbitals Can Be Ordered According to Their Energies
  104. 9.10: Molecular-Orbital Theory Does not Predict a Stable Diatomic Helium Molecule
  105. 9.11: Electrons Populate Molecular Orbitals According to the Pauli Exclusion Principle
  106. 9.12: Molecular Orbital Theory Predicts that Molecular Oxygen is Paramagnetic
  107. 9.E: The Chemical Bond- Diatomic Molecules (Exercises)
  108. 10: MathChapters
  109. 10.1: A- Complex Numbers
  110. 10.2: B- Probability and Statistics
  111. 10.3: C- Vectors
  112. 10.4: D- Spherical Coordinates
  113. 10.5: E- Determinants
  114. 10.6: F- Matrices
  115. 10.7: G- Numerical Methods
  116. 10.8: H- Partial Differentiation
  117. 10.9: I- Series and Limits
  118. 10.10: J- The Binomial Distribution and Stirling's Appromixation
  119. Back Matter
  120. Index
  121. Glossary
  122. Detailed Licensing