Graduate Quantum Mechanics Notes

Michael Fowler, University of Virginia

1. Reviewing Elementary Stuff...

  • Introduction
  • Early Quantum Mechanics
  • Wave Equations, Wavepackets, Superposition
  • The Uncertainty Principle
  • Electron in a Box

2. Some Essential Math

  • Fourier Series and Integrals, the Dirac Function
  • Linear Algebra
  • Function Spaces
  • Complex Variable, Stationary Path Integrals

3. Mostly 1-D Quantum Mechanics

  • 1-D Schrodinger Equation: Examples
  • General Uncertainty Principle
  • Energy-Time Uncertainty Principle
  • The Simple Harmonic Oscillator
  • Propagators and Representations

.

  • PDF
  • PDF
  • PDF
  • PDF
  • PDF

.

  • PDF
  • PDF
  • PDF
  • PDF

.

  • PDF
  • PDF
  • PDF
  • PDF
  • PDF
  • Coherent States
  • Path Integrals
  • Path Integrals for the SHO

4. Angular Momentum and Spin

  • Angular Momentum
  • Orbital Eigenfunctions: 2-D Case
  • Note on Curvilinear Coordinates
  • Orbital Eigenfunctions in 3-D
  • Spin
  • The Hydrogen Atom

5. Various Topics

  • Bosons and Fermions (undergrad)
  • Multielectron Atoms (undergrad)
  • Charged Particle in Magnetic Field
  • The Density Matrix

6. Approximate Methods

  • Variational Methods
  • PDF
  • PDF
  • PDF

.

  • PDF
  • PDF
  • PDF
  • PDF
  • PDF
  • PDF

.

  • PDF
  • PDF
  • PDF
  • PDF

.

  • PDF
  • The WKB Approximation

7. Perturbation Theory

  • Time-Independent Perturbation Theory
  • The Peierls Transition: an unexpected insulator
  • Van der Waals Forces between Atoms
  • The Interaction Representation
  • Time-Dependent Perturbation Theory
  • The Photoelectric Effect in Hydrogen
  • Quantizing Radiation

8. Scattering Theory

  • Scattering Theory
  • More Scattering Theory: Partial Waves
  • Scattering Amplitudes, Bound States, Resonances
  • Identical Particles: Symmetry and Scattering

Other Material...

  • Schrodinger Spreadsheets
  • Homeworks, exams, etc.
  • PDF

    .

  • PDF
  • PDF
  • PDF
  • PDF
  • PDF
  • PDF
  • PDF

.

  • PDF
  • PDF
  • PDF
  • PDF

.

  • .
  • .