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- 1: The Dawn of the Quantum Theory
- 1.1: Blackbody Radiation Cannot Be Explained Classically
- 1.2: Quantum Hypothesis used for Blackbody Radiation Law
- 1.3: Photoelectric Effect Explained with Quantum Hypothesis
- 1.4: The Hydrogen Atomic Spectrum
- 1.5: The Rydberg Formula and the Hydrogen Atomic Spectrum
- 1.6: Matter Has Wavelike Properties
- 1.7: de Broglie Waves can be Experimentally Observed
- 1.8: The Bohr Theory of the Hydrogen Atom
- 1.9: The Heisenberg Uncertainty Principle
- 1.E: The Dawn of the Quantum Theory (Exercises)
- 2: The Classical Wave Equation
- 3: The Schrödinger Equation & a Particle in a Box
- 3.1: The Schrödinger Equation
- 3.2: Linear Operators in Quantum Mechanics
- 3.3: The Schrödinger Equation is an Eigenvalue Problem
- 3.4: The Quantum Mechanical Free Particle
- 3.5: Wavefunctions Have a Probabilistic Interpretation
- 3.6: The Energy of a Particle in a Box is Quantized
- 3.7: Wavefunctions Must Be Normalized
- 3.8: The Average Momentum of a Particle in a Box is Zero
- 3.9B: Particle in a Finite Box and Tunneling (optional)
- 3.9: The Uncertainty Principle Redux - Estimating Uncertainties from Wavefunctions
- 3.10: A Particle in a Two-Dimensional Box
- 3.11: A Particle in a Three-Dimensional Box
- 3.E: The Schrödinger Equation and a Particle in a Box (Exercises)
- 4: Postulates and Principles of Quantum Mechanics
- 4.1: The Wavefunction Specifies the State of a System
- 4.2: Quantum Operators Represent Classical Variables
- 4.3: Observable Quantities Must Be Eigenvalues of Quantum Mechanical Operators
- 4.4: The Time-Dependent Schrödinger Equation
- 4.5: The Eigenfunctions of Operators are Orthogonal
- 4.6: Heisenburg Uncertainy Principle III - Commuting Operators
- 4.E: Postulates and Principles of Quantum Mechanics (Exercises)
- 5: The Harmonic Oscillator and the Rigid Rotor
- 5.1: A Harmonic Oscillator Obeys Hooke's Law
- 5.2: The Equation for a Harmonic-Oscillator Model of a Diatomic Molecule Contains the Reduced Mass of the Molecule
- 5.3: The Harmonic Oscillator is an Approximation
- 5.4: The Harmonic Oscillator Energy Levels
- 5.5: The Harmonic Oscillator and Infrared Spectra
- 5.6: The Harmonic-Oscillator Wavefunctions Involve Hermite Polynomials
- 5.7: Hermite Polynomials are either Even or Odd Functions
- 5.8: The Energy Levels of a Rigid Rotor
- 5.9: The Rigid Rotator is a Model for a Rotating Diatomic Molecule
- 5.E: The Harmonic Oscillator and the Rigid Rotor (Exercises)
- 6: The Hydrogen Atom
- 6.1: The Schrödinger Equation for the Hydrogen Atom Can Be Solved Exactly
- 6.2: The Wavefunctions of a Rigid Rotator are Called Spherical Harmonics
- 6.3: The Three Components of Angular Momentum Cannot be Measured Simultaneously with Arbitrary Precision
- 6.4: Hydrogen Atomic Orbitals Depend upon Three Quantum Numbers
- 6.5: s Orbitals are Spherically Symmetric
- 6.6: Orbital Angular Momentum and the p-orbitals
- 6.7: The Helium Atom Cannot Be Solved Exactly
- 6.E: The Hydrogen Atom (Exercises)
- 7: Approximation Methods
- 7.0: Slater's Rules for Shielding
- 7.1: The Variational Method
- 7.2: Linear Variational Method and the Secular Determinant
- 7.3: Trial Functions Can Be Linear Combinations of Functions with Variational Parameters
- 7.4: Perturbation Theory Expresses the Solutions in Terms of Solved Problems
- 7.E: Approximation Methods (Exercises)
- 8: Multielectron Atoms
- 8.1: Atomic and Molecular Calculations are Expressed in Atomic Units
- 8.2: Perturbation Theory and the Variational Method for Helium
- 8.3: Hartree-Fock Equations are Solved by the Self-Consistent Field Method
- 8.4: An Electron Has An Intrinsic Spin Angular Momentum
- 8.5: Wavefunctions must be Antisymmetric to Interchange of any Two Electrons
- 8.6: Antisymmetric Wave Functions can be Represented by Slater Determinants
- 8.7: Hartree-Fock Calculations Give Good Agreement with Experimental Data
- 8.8: Term Symbols Gives Detailed Descriptions of an Electron Configuration
- 8.8B: Multi-electron Considerations - A Closer Look at Helium
- 8.9: The Allowed Values of J - the Total Angular Momentum Quantum Number
- 8.10: Hund's Rules Determine the Term Symbols of the Ground Electronic States
- 8.11: Using Atomic Term Symbols to Describe Atomic Spectra
- 8.E: Multielectron Atoms (Exercises)
- 9: The Chemical Bond: Diatomic Molecules
- 9.1: The Born-Oppenheimer Approximation Simplifies the Molecular Schrödinger Equation
- 9.2: The H₂⁺ Prototypical Species
- 9.2B: Solving the H₂⁺ System Exactly (Optional)
- 9.3: The Overlap Integral
- 9.3B: Evaluating the Overlap Integral (Optional)
- 9.4: Chemical Bond Stability
- 9.5: Bonding and Antibonding Orbitals
- 9.6: A Simple Molecular-Orbital Treatment of H₂ Places Both Electrons in a Bonding Orbital
- 9.7: Molecular Orbitals Can Be Ordered According to Their Energies
- 9.8: Molecular-Orbital Theory Does not Predict a Stable Diatomic Helium Molecule
- 9.9: Electrons Populate Molecular Orbitals According to the Pauli Exclusion Principle
- 9.10: Molecular Orbital Theory Predicts that Molecular Oxygen is Paramagnetic
- 9.E: The Chemical Bond: Diatomic Molecules (Exercises)
- MathChapters
1: The Dawn of the Quantum Theory
2: The Classical Wave Equation
3: The Schrödinger Equation & a Particle in a Box
4: Postulates and Principles of Quantum Mechanics
5: The Harmonic Oscillator and the Rigid Rotor
6: The Hydrogen Atom
7: Approximation Methods
8: Multielectron Atoms
9: The Chemical Bond: Diatomic Molecules
MathChapters