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 
RydbergKleinRees: V(x) from EvJ 
9 
NumerovCooley 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. QuasiDegeneracy. Polyads. 
18 
Variational Method 
19 
Density Matrices I. Initial NonEigenstate Preparation, Evolution, Detection. 
20 
Density Matrices II. Quantum Beats. Subsystems and Partial Traces. 
III. Central Forces and Angular Momentum 

21 
3D Central Force I. Separation of Radial and Angular Momenta. 
22 
3D Central Force II. LeviCivita. ε_{ijk.} 
23 
Angular Momentum Matrix Elements from Commutation Rules 
24 
JMatrices 
25 
H^{SO} + H^{Zeeman}: Coupled vs. Uncoupled Basis Sets 
26 
JLSMJ>↔ LMLMS> by Ladders Plus Orthogonality 
27 
WignerEckart Theorem 
28 
Hydrogen Radial Wavefunctions 
29 
Pseudo OneElectron Atoms: Quantum Defect Theory 
IV. Many Particle Systems: Atoms, Coupled Oscillators, Periodic Lattice 

30 
Matrix Elements of ManyElectron Wavefunctions 
31 
Matrix Elements of OneElectron, F (i), and TwoElectron, G (i,j) Operators 
32 
Configurations and LSJ "Terms" (States) 
33 
ManyElectron LSJ Wavefunctions: L^{2} and S^{2} Matrices and Projection Operators 
34 
e^{2}/rij and Slater Sum Rule Method 
35 
Spin Orbit: ζ(N,L,S)↔ζnl 
36 
Holes. Hund's Third Rule. Landé gFactor via WE Theorem. 
37 
Infinite 1D Lattice I 
38 
Infinite 1D Lattice II. Band Structure. Effective Mass. 
39 
Catchup 
40 
Wrapup 