Synopsis of Quantum Mechanics

• The use of RLaB as an educational tool (1 week)
  • General setup
  • Interactive use and the pgraf graphics package
• The roots of quantum mechanics (2 weeks)
  • Review of relativistic kinematics and dynamics.
  • Wave and group velocity and waves in relativity (see packet_demo.r and propagator.r).
  • Louis de Broglie's analogy with optics.
  • Probability amplitude and flux.
• Simple problems (2 weeks)
  • Particle in a box (see symmwell.r).
  • Harmonic oscillator by shooting method. See shoot_demo.r.
  • Barrier penetration and scattering in 1-D (see scatter1_demo.r).
  • Polarization of light.
• Basic theory (3 weeks)
  • Big ideas of quantum mechanics
  • Hilbert space and Fourier transforms (see qcalc.r).
  • Wave functions and expectation values.
  • Observables, operators, and state vectors.
  • Position and momentum operators.
  • Harmonic oscillator (see ho_demo.r).
  • Time evolution and the energy (see evolve_demo.r and anho_demo.r).
  • Multiple compatible operators.
• Mid-term summary
• More one-dimensional problems -- (1 week)
  • Double potential well and degeneracy
  • Harmonic oscillator again
• Perturbation theory (1 week)
• Problems in higher dimensions (2 weeks)
  • Two-dimensional harmonic oscillator
  • Orbital angular momentum and the hydrogen atom
• Spin (1 week)
  • The Stern-Gerlach experiment
  • Angular momentum by operator methods
• Multiple particles (see ident.r) (1 week)
• Electromagnetism and quantum mechanics (1 week)