Quantum Chemistry

  1. Approximation Methods
    1. Variational Method
      1. Variational Principle
        1. Variational Theorem
          1. Upper Bound Property
            1. Physical Interpretation
            2. Linear Variational Method
              1. Trial Wavefunctions
                1. Variational Parameters
                  1. Optimization Procedures
                  2. Secular Equations
                    1. Matrix Formulation
                      1. Secular Determinant
                        1. Solution Methods
                        2. Applications
                          1. Helium Atom Ground State
                            1. Hydrogen Molecule Ion
                              1. Simple Molecules
                            2. Perturbation Theory
                              1. Time-Independent Perturbation Theory
                                1. Small Perturbations
                                  1. Expansion in Orders
                                  2. Non-Degenerate Perturbation Theory
                                    1. First-Order Energy Correction
                                      1. First-Order Wavefunction Correction
                                        1. Second-Order Energy Correction
                                        2. Degenerate Perturbation Theory
                                          1. Lifting of Degeneracy
                                            1. Correct Zero-Order Functions
                                              1. Matrix Diagonalization
                                              2. Applications
                                                1. Stark Effect
                                                  1. Zeeman Effect
                                                    1. Anharmonic Oscillator
                                                    2. Time-Dependent Perturbation Theory
                                                      1. Time-Dependent Hamiltonians
                                                        1. Transition Probabilities
                                                          1. Fermi's Golden Rule
                                                            1. Selection Rules

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                                                        3. Exactly Solvable Quantum Systems

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                                                        5. Multi-Electron Atoms