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