- (A) Introduction to quantum mechanics:

Scope and applicability of quantum mechanics

The Schrödinger equation - (B) History of quantum mechanics
- (C) Linear vector spaces:

Definitions

Inner products

Dual spaces and Dirac notation - (C) Operators:

Basic operator rules

Classes of operators: linear, hermitian, unitary, etc.

Commutators - (D) Postulates
- (E) Simple problems: particle in a box (1D and 3D), free particle

- (A) Harmonic oscillator

Vibrational (IR) spectroscopy, anharmonicity, group theory - (B) Heisenberg uncertainty relations
- (C) Angular momentum:

Commutation rules

Spherical harmonics

Ladder operators

Rigid rotor: a model for rotational (microwave) spectroscopy - (D) The Hydrogen atom and its electronic spectrum

- (A) Variational method:

Variational theorem

Equivalence of Raleigh-Ritz procedure and diagonalization - (B) Time-independent perturbation theory

- (A) Spin and ESR spectroscopy
- (B) Degenerate perturbation theory and the Stark effect in H atom
- (C) Time-dependent perturbation theory and the interaction of light with matter

- (A) The molecular Hamiltonian:

Born-Oppenheimer approximation - (B) Separation into electronic, vibrational, rotational terms
- (C) Introduction to Hartree-Fock theory:

Two-electron problem

Hartree products

Antisymmetry and Slater determinants

Generalization to -electrons

Self-consistent-field - (D) Introduction to correlated methods
- (E) Electronic structure of atoms
- (F) Electronic structure of diatomics
- (G) Electronic structure of polyatomics:

Walsh's rules - (H) Rovibronic spectroscopy and the Franck-Condon approximation