1-4 Experimental Evidence for Quantum Mechanics

Polarization of Light

Single Molecule Fluorescence
5-7 The Machinery of Quantum Mechanics

Hilbert Space

State Vectors


Operators and Eigenvalues
8-12 Exactly Solvable Problems

Operators and States in Real Space

Harmonic Oscillator

Position Representation and Wave Mechanics

Piecewise Constant Potentials
Problem set 1 due after Lec #8

Problem set 2 due after Lec #11

13-15 Matrix Mechanics

Vector Representation of States

Matrices as Operators

Interesting Matrix Properties

Discrete Variable Representation

Variational Method
Problem set 3 due after Lec #14

Problem set 4 due after Lec #17
16-18 Time Dependence

Energy Eigenstates and Stationary States

The Propagator

Time Dependence of Average Values

Matrix Representations of the Propagator

Example: Inversion of the Ammonia Molecule
Midterm exam handed out after Lec #18
19-20 Angular Momentum


Commutation Relations

21-22 Central Potentials

Spherical Polar Coordinates

Orbital Angular Momentum Operators

Spherical Harmonics

The Radial Equation

Hydrogen-like Atoms

Electron Spin
Midterm exam due after Lec #21
23-24 Addition of Angular Momenta

Coupled and Uncoupled Bases

Recursion Relations

The Triangle Rule
25 Wigner-Eckart Theorem

Spherical Tensors
26-28 Perturbation Theory Problem set 5 due after Lec #27
29-31 Identical Particles

The Product Basis

Symmetry Under Exchange

Two Electron Atoms


Perturbation Theory

Configuration Interaction
Problem set 5 due after Lec #31
32-34 The Born-Oppenheimer Approximation

The Adiabatic Approximation

The Coupled Channel Hamiltonian

Non-Adiabatic Effects

Diabatic States

Electron Transfer
35-38 The Hydrogen Molecule

Minimal Atomic Orbital Basis

Molecular Orbital Picture

Valence Bond Picture
Problem set 7 due after Lec #35

Final exam after Lec #38