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

QUIZ 1

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

QUIZ 2

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

QUIZ 3

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