Quantum Mechanics
Posted here are my notes for a course in quantum mechanics
at the graduate level.
I will update these notes regularly and put corrections in
as I find them, and you can always contact me
if you have corrections or comments.
You can download the notes here as one big file: (pdf, many MB).
Instructors may contact me for a version with
solutions to problems included.
If you use these notes for your class, please let me know!
Topics Covered:

Classical Mechanics: Review of variational principles

Axioms of Quantum Mechanics: Hilbert spaces, time evolution, quantization, representations, unitarity

Basic Examples: Free particle, infinite and finite square wells, square barriers, tunneling and reflection

DoubleWell Potential: tunneling/Rabi oscillations, quantum Zeno effect, avoided crossings, adiabatic passage

Harmonic Oscillator: Ladder operators, coherent states, classical limit

Semiclassics: Ehrenfest equations, standard quantum limit, WKB approximation

Angular Momentum: ladder operators, addition, rotations, irreducible tensor operators, WignerEckart theorem, multipole radiation

ThreeDimensional Particles: Free particle, hydrogen atom

Spin: Bloch sphere, precession, entanglement, EPR paradox, Bell theorem

Multiple Particles: Density operator, entanglement, cloning, teleportation, indistinguishability

TimeIndependent Perturbation Theory: Resolvent operator, Stark effects, degeneracy, fine structure, hyperfine structure, Zeeman effect

TimeDependent Perturbation Theory: Dyson series, Green functions, Rabi oscillations, rotatingwave approximation, Bragg diffraction, ac polarizability

LinearResponse Theory: Kubo formula, causality, fluctuationdissipation theorem, Johnson noise

Continuum Transitions: Fermi golden rule, spontaneous decay, photoionization

Path Integration: propagator, functional integration, classical limit, Gel'fandYaglom method, van VleckMorette determinant