I. One Dimensional Problems
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
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
21 3-D Central Force I. Separation of Radial and Angular Momenta.
22 3-D Central Force II. Levi-Civita. εijk.
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
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
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