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CHEM 110A: Introduction to Quantum Mechanics

Nguồn ngoài

CHEM 110A: Introduction to Quantum Mechanics

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

Chemistry
Tác giả
Delmar Larsen
Nhà xuất bản
University of California, Davis
Nguồn
LibreTexts
Giấy phép
CC BY-NC-SA
Ngôn ngữ
EN
Danh mục
Khoa học cơ bản
Đọc trực tuyến Tải PDF (nguồn mở)
Mục lục· 113 mục
  1. 01: The Dawn of the Quantum Theory
  2. 1.01: Blackbody Radiation Cannot Be Explained Classically
  3. 1.02: Quantum Hypothesis used for Blackbody Radiation Law
  4. 1.03: Photoelectric Effect Explained with Quantum Hypothesis
  5. 1.04: The Hydrogen Atomic Spectrum
  6. 1.05: The Rydberg Formula and the Hydrogen Atomic Spectrum
  7. 1.06: Matter Has Wavelike Properties
  8. 1.07: de Broglie Waves can be Experimentally Observed
  9. 1.08: The Bohr Theory of the Hydrogen Atom
  10. 1.09: The Heisenberg Uncertainty Principle
  11. 1.E: The Dawn of the Quantum Theory (Exercises)
  12. 02: The Classical Wave Equation
  13. 2.01: The One-Dimensional Wave Equation
  14. 2.02: The Method of Separation of Variables
  15. 2.03: Oscillatory Solutions to Differential Equations
  16. 2.04: The General Solution is a Superposition of Normal Modes
  17. 2.05: A Vibrating Membrane
  18. 2.E: The Classical Wave Equation (Exercises)
  19. 03: The Schrodinger Equation and the Particle-in-a-Box Model
  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: The Uncertainty Principle Redux - Estimating Uncertainties from Wavefunctions
  29. 3.10: Particle in a Finite Box and Tunneling (Optional)
  30. 3.11: A Particle in a Two-Dimensional Box
  31. 3.12: A Particle in a Three-Dimensional Box
  32. 3.E: The Schrodinger Equation and a Particle in a Box (Exercises)
  33. 3.I: Interactive Worksheets
  34. 3.I.1: Free Particle (Python Notebook)
  35. 3.I.2: Particle in an Infinite Potential Box (Python Notebook)
  36. 3.I.3: Particle in a Finite Potential Box (Python Notebook)
  37. 04: Postulates and Principles of Quantum Mechanics
  38. 4.01: The Wavefunction Specifies the State of a System
  39. 4.02: Quantum Operators Represent Classical Variables
  40. 4.03: Observable Quantities Must Be Eigenvalues of Quantum Mechanical Operators
  41. 4.04: The Time-Dependent Schrodinger Equation
  42. 4.05: The Eigenfunctions of Operators are Orthogonal
  43. 4.06: Heisenburg Uncertainy Principle III - Commuting Operators
  44. 4.E: Postulates and Principles of Quantum Mechanics (Exercises)
  45. 05: The Harmonic Oscillator and the Rigid Rotor
  46. 5.01: A Harmonic Oscillator Obeys Hooke's Law
  47. 5.02: The Equation for a Harmonic-Oscillator Model of a Diatomic Molecule Contains the Reduced Mass of the Molecule
  48. 5.03: The Harmonic Oscillator is an Approximation
  49. 5.04: The Harmonic Oscillator Energy Levels
  50. 5.05: The Harmonic Oscillator and Infrared Spectra
  51. 5.06: The Harmonic-Oscillator Wavefunctions Involve Hermite Polynomials
  52. 5.07: Hermite Polynomials are either Even or Odd Functions
  53. 5.08: The Energy Levels of a Rigid Rotor
  54. 5.09: The Rigid Rotator is a Model for a Rotating Diatomic Molecule
  55. 5.E: The Harmonic Oscillator and the Rigid Rotor (Exercises)
  56. 5.I: Interactive Worksheets
  57. 5.2I: Spherical Harmonics Visualization
  58. 5.I1: Simple Harmonic Oscillator - Plotting Eigenstates
  59. 06: The Hydrogen Atom
  60. 6.01: The Schrodinger Equation for the Hydrogen Atom Can Be Solved Exactly
  61. 6.02: The Wavefunctions of a Rigid Rotator are Called Spherical Harmonics
  62. 6.03: The Three Components of Angular Momentum Cannot be Measured Simultaneously with Arbitrary Precision
  63. 6.04: Hydrogen Atomic Orbitals Depend upon Three Quantum Numbers
  64. 6.05: s Orbitals are Spherically Symmetric
  65. 6.06: Orbital Angular Momentum and the p-orbitals
  66. 6.07: The Helium Atom Cannot Be Solved Exactly
  67. 6.E: The Hydrogen Atom (Exercises)
  68. 07: Approximation Methods
  69. 7.01: Slater's Rules for Shielding
  70. 7.02: The Variational Method
  71. 7.03: Linear Variational Method and the Secular Determinant
  72. 7.04: Trial Functions Can Be Linear Combinations of Functions with Variational Parameters
  73. 7.05: Perturbation Theory Expresses the Solutions in Terms of Solved Problems
  74. 7.E: Approximation Methods (Exercises)
  75. 08: Multielectron Atoms
  76. 8.01: Atomic and Molecular Calculations are Expressed in Atomic Units
  77. 8.02: Perturbation Theory and the Variational Method for Helium
  78. 8.03: Hartree-Fock Equations are Solved by the Self-Consistent Field Method
  79. 8.04: An Electron Has An Intrinsic Spin Angular Momentum
  80. 8.05: Wavefunctions must be Antisymmetric to Interchange of any Two Electrons
  81. 8.06: Antisymmetric Wave Functions can be Represented by Slater Determinants
  82. 8.07: Hartree-Fock Calculations Give Good Agreement with Experimental Data
  83. 8.08: Term Symbols Gives Detailed Descriptions of an Electron Configuration
  84. 8.09: Multi-electron Considerations - A Closer Look at Helium
  85. 8.10: The Allowed Values of J - the Total Angular Momentum Quantum Number
  86. 8.11: Hund's Rules Determine the Term Symbols of the Ground Electronic States
  87. 8.12: Using Atomic Term Symbols to Describe Atomic Spectra
  88. 8.E: Multielectron Atoms (Exercises)
  89. 09: The Chemical Bond- Diatomic Molecules
  90. 9.01: The Born-Oppenheimer Approximation Simplifies the Molecular Schrodinger Equation
  91. 9.02: The H Prototypical Species
  92. 9.03: Solving the H System Exactly (Optional)
  93. 9.04: The Overlap Integral
  94. 9.05: Evaluating the Overlap Integral (Optional)
  95. 9.06: Chemical Bond Stability
  96. 9.07: Bonding and Antibonding Orbitals
  97. 9.08: A Simple Molecular-Orbital Treatment of H Places Both Electrons in a Bonding Orbital
  98. 9.09: Molecular Orbitals Can Be Ordered According to Their Energies
  99. 9.10: Molecular-Orbital Theory Does not Predict a Stable Diatomic Helium Molecule
  100. 9.11: Electrons Populate Molecular Orbitals According to the Pauli Exclusion Principle
  101. 9.12: Molecular Orbital Theory Predicts that Molecular Oxygen is Paramagnetic
  102. 9.E: The Chemical Bond- Diatomic Molecules (Exercises)
  103. 10: MathChapters
  104. 10.01: A- Complex Numbers
  105. 10.02: B- Probability and Statistics
  106. 10.03: C- Vectors
  107. 10.04: D- Spherical Coordinates
  108. 10.05: E- Determinants
  109. 10.06: F- Matrices
  110. 10.07: G- Numerical Methods
  111. 10.08: H- Partial Differentiation
  112. 10.09: I- Series and Limits
  113. 10.10: J- The Binomial Distribution and Stirling's Appromixation