Quantum Mechanics I

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