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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 |
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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 |
