Calendar

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