Ses # | topics | key dates |
---|---|---|
1–9: One-Dimensional Problems | ||
1 | Course Outline; Free Particle; Motion? | |
2 | Infinite Box, \(\delta(x)\) Well, \(\delta(x)\) Barrier | |
3 | \({\mid{\Psi(x,t)}\mid}^2\): Motion, Position, Spreading, Gaussian Wavepacket | |
4 | Stationary Phase and Gaussian Wavepackets | |
5 | Continuum Normalization | Problem Set 1 due |
6 | Linear \(V(x)\); JWKB Approximation and Quantization | |
7 | JWKB Quantization Condition | |
8 | Rydberg-Klein-Rees: \(V(x)\) from \(E_{vJ}\) | 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 \(\varepsilon_{ijk}\) | |
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\(\rangle\) and ⎜LMLMS\(\rangle\) by Ladders plus Orthogonality | |
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, \(F(i)\), and Two-Electron, \(G(i,j)\) Operators | |
32 | Configurations and Resultant L-S-J “Terms” (States) | |
33 | L-S Terms via L2, S2 and Projection | |
34 | \(e^2/r_{ij}\) and Slater Sum Rule Method | Problem Set 9 due |
35 | Spin Orbit: Many Electron ζ(N,L,S)↔Single Orbital ζ\(_{nl}\) Coupling Constants | |
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 |