I. One Dimensional Problems
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1 |
Course Outline. Free Particle. Motion? |
2 |
Infinite Box, δ(x) Well, δ(x) Barrier |
3 |
|Ψ(x,t)|2: Motion, Position, Spreading, Gaussian Wavepacket |
4 |
Information Encoded in Ψ(x,t). Stationary Phase. |
5 |
Continuum Normalization |
6 |
Linear V(x). JWKB Approximation and Quantization. |
7 |
JWKB Quantization Condition |
8 |
Rydberg-Klein-Rees: V(x) from EvJ |
9 |
Numerov-Cooley Method |
II. Matrix Mechanics
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10 |
Matrix Mechanics |
11 |
Eigenvalues and Eigenvectors. DVR Method. |
12 |
Matrix Solution of Harmonic Oscillator (Ryan Thom Lectures) |
13 |
Creation (a† ) and Annihilation (a) Operators |
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 |
19 |
Density Matrices I. Initial Non-Eigenstate Preparation, Evolution, Detection. |
20 |
Density Matrices II. Quantum Beats. Subsystems and Partial Traces. |
III. Central Forces and Angular Momentum |
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21 |
3-D Central Force I. Separation of Radial and Angular Momenta. |
22 |
3-D Central Force II. Levi-Civita. εijk.
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23 |
Angular Momentum Matrix Elements from Commutation Rules |
24 |
J-Matrices |
25 |
HSO + HZeeman: Coupled vs. Uncoupled Basis Sets |
26 |
|JLSMJ>↔ |LMLMS> by Ladders Plus Orthogonality |
27 |
Wigner-Eckart Theorem |
28 |
Hydrogen Radial Wavefunctions |
29 |
Pseudo One-Electron Atoms: Quantum Defect Theory |
IV. Many Particle Systems: Atoms, Coupled Oscillators, Periodic Lattice |
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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 L-S-J "Terms" (States) |
33 |
Many-Electron L-S-J Wavefunctions: L2 and S2 Matrices and Projection Operators |
34 |
e2/rij and Slater Sum Rule Method |
35 |
Spin Orbit: ζ(N,L,S)↔ζnl
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36 |
Holes. Hund's Third Rule. Landé g-Factor via W-E Theorem. |
37 |
Infinite 1-D Lattice I |
38 |
Infinite 1-D Lattice II. Band Structure. Effective Mass. |
39 |
Catch-up |
40 |
Wrap-up |