Ses # | topics | key dates |
---|---|---|
1–9: One-Dimensional Problems | ||
1 | Course Outline; Free Particle; Motion? | |
2 |
Infinite Box, |
|
3 |
|
|
4 | Stationary Phase and Gaussian Wavepackets | |
5 | Continuum Normalization | Problem Set 1 due |
6 |
Linear |
|
7 | JWKB Quantization Condition | |
8 |
Rydberg-Klein-Rees: |
Problem Set 2 due |
9 | Numerov-Cooley Method: 1-D Schrödinger Equation | |
10–19: Matrix Mechanics | ||
10 | Matrix Mechanics | Problem Set 3 due |
11 | Eigenvalues, Eigenvectors, and Discrete Variable Representation (DVR) | |
12 | Matrix Solution of Harmonic Oscillator | |
13 |
End of Matrix Solution of H-O, and Feel the Power of the a and a† Operators |
Problem Set 4 due |
14 | Perturbation Theory I; Begin Cubic Anharmonic Perturbation | |
15 | Perturbation Theory II; Cubic and Morse Oscillators | |
16 | Perturbation Theory III; Transition Probability; Wavepacket; Degeneracy | |
17 | Perturbation Theory IV; Recurrences; Dephasing; Quasi-Degeneracy; Polyads | |
18 | Variational Method | Problem Set 5 due |
19 | Density Matrices I; Initial Non-Eigenstate Preparation, Evolution, Detection | |
20–29: Central Forces and Angular Momentum | ||
20 | Density Matrices II; Quantum Beats; Subsystems and Partial Traces | |
21 | 3-D Central Force Problems I; Separation of Radial and Angular Momenta | Take-Home Mid-term Exam due |
22 |
3-D Central Force Problems II; Levi-Civita |
|
23 | Angular Momentum Matrix Elements from Commutation Rules | |
24 | J-Matrices | Problem Set 6 due |
25 | HSO + HZeeman: Coupled vs. Uncoupled Basis Sets | |
26 |
HSO + HZeeman in ⎜JLSMJ |
|
27 | Wigner-Eckart Theorem | Problem Set 7 due |
28 | Hydrogen Radial Wavefunctions | |
29 | Begin Many e- Atoms: Quantum Defect Theory | Problem Set 8 due |
30–39: Many Particle Systems: Atoms, Coupled Oscillators, Periodic Lattice | ||
30 | Matrix Elements of Many-Electron Wavefunctions | |
31 |
Matrix Elements of One-Electron, |
|
32 | Configurations and Resultant L-S-J “Terms” (States) | |
33 | L-S Terms via L2, S2 and Projection | |
34 |
|
Problem Set 9 due |
35 |
Spin Orbit: Many Electron ζ(N,L,S)↔Single Orbital ζ |
|
36 | Holes; Hund’s Third Rule; Landé g-Factor via W-E Theorem | |
37 | Infinite 1-D Lattice I | Problem Set 10 due |
38 | Infinite 1-D Lattice II; Band Structure; Effective Mass | |
39 | One-Dimensional Lattice: Weak-Coupling Limit | |
Take-Home Final Exam |
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