- Falling: Motion in a Linear Potential
- One Dimensional
- classical motion: PE, turning points,
*z(t)*, etc. - length and energy scales
- Schrödinger's equation solution: Airy function
- graphs of solutions
- connecting classical variables and the wavefunction: WKB approximation
- QM "motion", Heisenberg uncertainty relation
- mathematical details of the above: superposition, time dependence
- approximation methods: WKB, Rayleigh-Ritz (variational), perturbation theory

- classical motion: PE, turning points,
- Two Dimensional
- Problems

- One Dimensional
- Simple Harmonic Oscillator
- One Dimensional
- classical motion: PE, turning points,
*x(t)*, etc. - length and energy scales
- Schrödinger's equation solution: Hermite polynomials
- graphs of solutions
- connecting classical variables and the wavefunction: WKB approximation
- QM "motion", Heisenberg uncertainty relation
- mathematical details of the above: superposition, time dependence
- raising and lowering operators

- classical motion: PE, turning points,
- Two Dimensional
- Three Dimensional
- Problems

- One Dimensional
- Hydrogen Atom
- classical motion: PE, turning points, Kepler's Laws,
*r(t)*, etc. - length and energy scales
- Schrödinger's equation solutions: Laguerre polynomials
- radial plots of wavefunctions
- visualizing the wavefunctions in 3D
- two electron atoms
- exchange symmetry and spin-statistics
- spin-statistics theorem
- Aufbau: building up multi-electron atoms
- Stark effect
- crystal field theory
- chemical bonding
- problems

- classical motion: PE, turning points, Kepler's Laws,
- Square Wells
- One Dimensional
- Two Dimensional
- Three Dimensional
- infinite 3D rectangular square-well:
*xyz*separation - spherical square-well: spherical Bessel functions
- visualizing the wavefunctions in 3D
- spherical finite square-wells: bound states
- scattering from spherical infinite barrier: solid angle, phase shifts, cross-section
- scattering from spherical finite square-well: glory, resonance

- infinite 3D rectangular square-well:
- Problems

- Delta Function Potentials
- Electrons in a Lattice: Band Structure
- lattice & lattice vectors; classical motion: PE, turning points, etc.
- Block wavefunctions; Schrödinger's equation; length and energy scales
- reciprocal lattice space
- grids: approximation to Schrödinger's equation in real space
- band structure in an empty lattice (i.e., free particle)
- numerical and exact solution to grided empty lattice
- numerical band structure for various potentials
- wavefunctions for various potentials
- Plane wave expansion aproximation
- discussion: relationship to classical considerations
- Problems

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