Content
- Page ID
- 9831
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0. Reviews of mathematics, as necessary
1. Early Evidence of Quantum Mechanics
- Black body radiation
- Photoelectric effect
- De Broglie equation
- Bohr's atom
- Uncertainty principle
2. Classical Wave Equation
3. Schrödinger Equation
- Wavefunctions
- Linear operators
- Eigenfunction problems
- Probability and wavefunction normalization
- Quantization
4. Postulates of Quantum Mechanics
- Postulate 1: The Wavefunction
- Postulate 2: Observables and operators
- Postulate 3: Observables and eigenfunction equations
- Postulate 4: Expectation values of observables
- Postulate 5: Time evolution of the wavefunction
- Orthogonal Eigenfunctions
- Hermitian operators
- Commutation and uncertainty
5. Application of the postulates of quantum mechanics
- Behavior of a free particle
- Particle in a 1-D and 3-D box
6. Quantum Mechanics and Nanochemistry
- Quantum confinement
- Tunnelling Phenomena
7. Molecular Vibration
- Classical Harmonic Oscillator
- Quantum Mechanical Oscillator
- Hermite Polynomials
8. Angular Momentum
- Quantum Mechanical treatment of angular momentum
- Legendre Polynomials
- Spherical harmonics
9. Molecular rotation
- Classical Rigid Rotor
- Quantum Mechanical treatment of a 2-D and 3-D Rigid Rotor
10. Spectroscopy
- Energy level populations
- Selection Rules
- Vibrational and Rotational Spectroscopy
11. The Hydrogen Atom
12. Multi-electron Atoms and Approximation Methods
- New Hamiltonian
- Variational Theory
- Trial functions
- Secular determinants
- Perturbation Theory
- Towards computational chemistry