5.73 | Fall 2005 | Graduate

Introductory Quantum Mechanics I

Lecture Notes

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


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)


Commutation Relations


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


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

As Taught In
Fall 2005
Learning Resource Types
Exams with Solutions
Lecture Notes
Problem Sets with Solutions