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Chemistry LibreTexts

Content

0. Reviews of mathematics, as necessary

1. Early Evidence of Quantum Mechanics

  1. Black body radiation
  2. Photoelectric effect
  3. De Broglie equation
  4. Bohr's atom
  5. Uncertainty principle

2. Classical Wave Equation

3. Schrödinger Equation

  1. Wavefunctions
  2. Linear operators
  3. Eigenfunction problems
  4. Probability and wavefunction normalization
  5. Quantization

4. Postulates of Quantum Mechanics

  1. Postulate 1: The Wavefunction
  2. Postulate 2: Observables and operators
  3. Postulate 3: Observables and eigenfunction equations
  4. Postulate 4: Expectation values of observables
  5. Postulate 5: Time evolution of the wavefunction
  6. Orthogonal Eigenfunctions
  7. Hermitian operators
  8. Commutation and uncertainty

5. Application of the postulates of quantum mechanics

  1. Behavior of a free particle
  2. Particle in a 1-­D and 3-­D box

6. Quantum Mechanics and Nanochemistry

  1. Quantum confinement
  2. Tunnelling Phenomena

7. Molecular Vibration

  1. Classical Harmonic Oscillator
  2. Quantum Mechanical Oscillator
  3. Hermite Polynomials

8. Angular Momentum

  1. Quantum Mechanical treatment of angular momentum
  2. Legendre Polynomials
  3. Spherical harmonics

9. Molecular rotation

  1. Classical Rigid Rotor
  2. Quantum Mechanical treatment of a 2-­D and 3-­D Rigid Rotor

10. Spectroscopy

  1. Energy level populations
  2. Selection Rules
  3. Vibrational and Rotational Spectroscopy

11. The Hydrogen Atom

12. Multi-­electron Atoms and Approximation Methods

  1. New Hamiltonian
  2. Variational Theory
  3. Trial functions
  4. Secular determinants
  5. Perturbation Theory
  6. Towards computational chemistry