Lecture Notes

Lec # TOPICS
1-4 Experimental Evidence for Quantum Mechanics ( PDF )

Polarization of Light

Single Molecule Fluorescence

5-7 The Machinery of Quantum Mechanics ( PDF )

Hilbert Space

State Vectors

Bra-Ket

Operators and Eigenvalues

8-12 Exactly Solvable Problems ( PDF )

Operators and States in Real Space

Harmonic Oscillator

Position Representation and Wave Mechanics

Piecewise Constant Potentials

13-15 Matrix Mechanics ( PDF )

Vector Representation of States

Matrices as Operators

Interesting Matrix Properties

Discrete Variable Representation

Variational Method

16-18 Time Dependence ( PDF )

Energy Eigenstates and Stationary States

The Propagator

Time Dependence of Average Values

Matrix Representations of the Propagator

Example: Inversion of the Ammonia Molecule

19-20 Angular Momentum ( PDF )

Rotations

Commutation Relations

Eigenstates

21-22 Central Potentials ( PDF )

Spherical Polar Coordinates

Orbital Angular Momentum Operators

Spherical Harmonics

The Radial Equation

Hydrogen-like Atoms

Electron Spin

23-24 Addition of Angular Momenta ( PDF )

Coupled and Uncoupled Bases

Recursion Relations

The Triangle Rule

25 Wigner-Eckart Theorem ( PDF )

Spherical Tensors

26-28 Perturbation Theory ( PDF )
29-31 Identical Particles ( PDF )

The Product Basis

Symmetry Under Exchange

Two Electron Atoms

Hartree-Fock

Perturbation Theory

Configuration Interaction

32-34 The Born-Oppenheimer Approximation ( PDF )

The Adiabatic Approximation

The Coupled Channel Hamiltonian

Non-Adiabatic Effects

Diabatic States

Electron Transfer

35-38 The Hydrogen Molecule ( PDF )

Minimal Atomic Orbital Basis

Molecular Orbital Picture

Valence Bond Picture

Course Info

Learning Resource Types

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