1: Intro and some history
2: ODEs
3: PDEs and Fourier Transforms
4: Gaussian and the "Heisenberg Uncertainty Principle"
5: Differential eigenvalue problem and finite differences
6: Matrix eigenvalues and eigenvectors, Hermitian conjugate
7: Matter Wave Interference and the Schrödinger Equation
8: Free particle Wavefunction: plane wave and time evolution
9: Observables and uncertainty
10: Time-Independent Schrödinger Eqn and particle in a box
11: Finite quantum well, boundary conditions, and finite differences
12: Double QW and attractive delta potential
13: Periodic potential and bandstructure
14: Harmonic Oscillator: Ladder operators
15: Harmonic Oscillator: Raising from the ground state; Numerical results
16: Harmonic Oscillator: Uncertainty and Correspondence principle
17: Harmonic Oscillator: "Brute Force" and Hermite Polynomials
18: Scattering: Transmission and Reflection Coefs
19: Scattering from delta potential and multiple interfaces
20: Transfer matrix method
21: Tunneling, Resonance, and emergence of bands
22: Transmission Calculation in Finite Differences I
23: Transmission Calculation in Finite Differences II
24: Current-Voltage Relations
25: I-V in 2D
26: Hilbert space and Dirac notation
27: 3D Cartesian coords (infinite cubical well)
28: 3D finite differences
29: Broken Symmetry, Kronecker product, and 3D Harmonic Oscillator
30: Classical wave equation beyond 1 dimension
31: Waves on the surface of a sphere
32: Quantum mechanics in spherically-symmetric potentials
33: Infinite spherical well
34: Classical and Semiclassical Bohr model
35: Hydrogen atom radial equation
36: Angular momentum z-component operator and Zeeman effect, spin