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Introduction to Quantum Mechanics

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Introduction to Quantum Mechanics

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.

Chemistry
Author
Delmar Larsen
Publisher
University of California, Davis
Source
LibreTexts
License
CC BY-NC-SA
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 106 sections
  1. 01: The Dawn of the Quantum Theory
  2. 1.1: Blackbody Radiation Cannot Be Explained Classically
  3. 1.2: Quantum Hypothesis used for Blackbody Radiation Law
  4. 1.3: Photoelectric Effect Explained with Quantum Hypothesis
  5. 1.4: The Hydrogen Atomic Spectrum
  6. 1.5: The Rydberg Formula and the Hydrogen Atomic Spectrum
  7. 1.6: Matter Has Wavelike Properties
  8. 1.7: de Broglie Waves can be Experimentally Observed
  9. 1.8: The Bohr Theory of the Hydrogen Atom
  10. 1.9: The Heisenberg Uncertainty Principle
  11. 1.E: The Dawn of the Quantum Theory (Exercises)
  12. 02. The Classical Wave Equation
  13. 2.1: The One-Dimensional Wave Equation
  14. 2.2: The Method of Separation of Variables
  15. 2.3: Oscillatory Solutions to Differential Equations
  16. 2.4: The General Solution is a Superposition of Normal Modes
  17. 2.5: A Vibrating Membrane
  18. 2.E: The Classical Wave Equation (Exercises)
  19. 03. The Schrodinger Equation and a Particle In a Box
  20. 3.01: The Schrodinger Equation
  21. 3.02: Linear Operators in Quantum Mechanics
  22. 3.03: The Schrodinger Equation is an Eigenvalue Problem
  23. 3.04: The Quantum Mechanical Free Particle
  24. 3.05: Wavefunctions Have a Probabilistic Interpretation
  25. 3.06: The Energy of a Particle in a Box is Quantized
  26. 3.07: Wavefunctions Must Be Normalized
  27. 3.08: The Average Momentum of a Particle in a Box is Zero
  28. 3.09: Particle in a Finite Box (and Tunneling)
  29. 3.09: The Uncertainty Principle Redux
  30. 3.10: A Particle in a Two-Dimensional Box
  31. 3.11: A Particle in a Three-Dimensional Box
  32. 3.E: The Schrodinger Equation and a Particle in a Box (Exercises)
  33. 04. Postulates and Principles of Quantum Mechanics
  34. 4.1: The Wavefunction Specifies the State of a System
  35. 4.2: Quantum Operators Represent Classical Variables
  36. 4.3: Observable Quantities Must Be Eigenvalues of Quantum Mechanical Operators
  37. 4.4: The Time-Dependent Schrodinger Equation
  38. 4.5: The Eigenfunctions of Operators are Orthogonal
  39. 4.6: Heisenburg Uncertainy Principle III - Commuting Operators
  40. 4.E: Postulates and Principles of Quantum Mechanics (Exercises)
  41. 05. The Harmonic Oscillator and the Rigid Rotator: Two Spectroscopic Models
  42. 5.1: A Harmonic Oscillator Obeys Hooke's Law
  43. 5.2: The Equation for a Harmonic-Oscillator Model of a Diatomic Molecule Contains the Reduced Mass of the Molecule
  44. 5.3: The Harmonic Oscillator is an Approximation
  45. 5.4: The Harmonic Oscillator Energy Levels
  46. 5.5: The Harmonic Oscillator and Infrared Spectra
  47. 5.6: The Harmonic-Oscillator Wavefunctions Involve Hermite Polynomials
  48. 5.7: Hermite Polynomials are either Even or Odd Functions
  49. 5.8: The Energy Levels of a Rigid Rotor
  50. 5.9: The Rigid Rotator is a Model for a Rotating Diatomic Molecule
  51. 5.E: The Harmonic Oscillator and the Rigid Rotor (Exercises)
  52. 06: The Hydrogen Atom
  53. 6.01: The Schrodinger Equation for the Hydrogen Atom Can Be Solved Exactly
  54. 6.02: The Wavefunctions of a Rigid Rotator Are Called Spherical Harmonics
  55. 6.03: The Precise Values of the Three Components of Angular Momentum Cannot Be Measured Simultaneously
  56. 6.04: Hydrogen Atomic Orbitals Depend upon Three Quantum Numbers
  57. 6.05: s Orbitals Are Spherically Symmetric
  58. 6.06: Orbital Angular Momentum and the p-orbitals
  59. 6.07: The Helium Atom Cannot Be Solved Exactly
  60. 6.E: The Hydrogen Atom (Exercises)
  61. 07. Approximation Methods
  62. 7.0: Slater's Rules for Shielding
  63. 7.1: The Variational Method
  64. 7.2: Linear Variational Method and the Secular Determinant
  65. 7.3: Trial Functions Can Be Linear Combinations of Functions with Variational Parameters
  66. 7.4: Perturbation Theory Expresses the Solutions in Terms of Solved Problems
  67. 7.E: Approximation Methods (Exercises)
  68. 08: Multielectron Atoms
  69. 8.01: Atomic and Molecular Calculations Are Expressed in Atomic Units
  70. 8.02: perturbation Theory and the Variational Method
  71. 8.03: Hartree-Fock Equations Are Solved by the Self-Consistent Field Method
  72. 8.04: An Electron Has An Intrinsic Spin Angular Momentum
  73. 8.05: Wave Functions Must Be Antisymmetric in the Interchange of Any Two Electrons
  74. 8.06: Antisymmetric Wave Functions Can Be Represented by Slater Determinants
  75. 8.07: Hartree-Fock Calculations Give Good Agreement with Experimental Data
  76. 8.08: A Term Symbol Gives a Detailed Description of an Electron Configuration
  77. 8.08B: Multi-electron Considerations - A Closer Look at Helium
  78. 8.09: The Allowed Values of J
  79. 8.10: Hund's Rules Determine the Term Symbols of the Ground Electronic States
  80. 8.11: Using Atomic Term Symbols to Describe Atomic Spectra
  81. 8.E: Multielectron Atoms (Exercises)
  82. 09: The Chemical Bond: Diatomic Molecules
  83. 09.1: The Born-Oppenheimer Approximation Simplifies the Schrodinger Equation for Molecules
  84. 09.2: The H Prototypical Species
  85. 09.2B: Solving the H System Exactly
  86. 09.3: The Overlap Integral
  87. 09.3B: Evaluating the Overlap Integral
  88. 09.4: Chemical Bond Stability
  89. 09.5: Bonding and Antibonding Orbitals
  90. 09.6: A Simple Molecular-Orbital Treatment of H2 Places Both Electrons in a Bonding Orbital
  91. 09.7: Molecular Orbitals Can Be Ordered According to Their Energies
  92. 09.8: Molecular-Orbital Theory Predicts that a Stable Diatomic Helium Molecule Does Not Exist
  93. 09.9: Electrons Are Placed into Molecular Orbitals in Accord with the Pauli Exclusion Principle
  94. 9.10: Molecular Orbital Theory Predicts that Molecular Oxygen is Paramagnetic
  95. 9.E: The Chemical Bond: Diatomic Molecules (Exercises)
  96. MathChapters
  97. A: Complex Numbers
  98. B: Probability and Statistics
  99. C: Vectors
  100. D: Spherical Coordinates
  101. E: Determinants
  102. F: Matrices
  103. G: Numerical Methods
  104. H: Partial Differentiation
  105. I: Series and Limits
  106. J: The Binomial Distribution and Stirling's Appromixation