Quantum Chemistry

1. Mathematical formulation of Quantum Mechanics - Operators and their properties. Dirac notation.
2. Postulates of Quantum Mechanics and measurement theory - The uncertainty principle. Quantum mechanics paradoxes: the Einstein-Podolsky-Rosen paradox and Schrödinger's cat.
3. The free particle and the construction of a wave packet.
4. Treatment of the harmonic oscillator using creation and annihilation operators.
5. General theory of angular momentum and angular momentum addition.
6. Spin angular momentum - Spin eigenfunctions for an N-electron system and their use in writing resonance structures. Measurement theory in the case of spin. The simplest example of an entangled state and its significance.
7. The hydrogen atom - Solving the Schrödinger equation for the simplest chemical system.
8. The variational principle and an introduction to perturbation methods.
9. Use of determinants to introduce antisymmetry - Calculation of matrix elements of the Hamiltonian operator for orthogonal orbitals and a brief mention of the non-orthogonal case.
10. The Hartree-Fock wavefunction - Derivation of the Hartree-Fock and Roothan equations.
11. Introduction to the electronic correlation problem and Density Functional Theory (DFT) - Their application in chemical modeling.
12. The density operator - Description of pure states and statistical mixtures. Possibility of describing a subsystem.
13. The formalism of second quantization.