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Introductory Quantum Mechanics I >> Content Detail



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Calendar

This calendar provides the lecture topics for the course.





LEC #TOPICS
I. One Dimensional Problems
1Course Outline. Free Particle. Motion?
2Infinite Box, δ(x) Well, δ(x) Barrier
3|Ψ(x,t)|2: Motion, Position, Spreading, Gaussian Wavepacket
4Information Encoded in Ψ(x,t). Stationary Phase.
5Continuum Normalization
6Linear V(x). JWKB Approximation and Quantization.
7JWKB Quantization Condition
8Rydberg-Klein-Rees: V(x) from EvJ
9Numerov-Cooley Method
II. Matrix Mechanics
10Matrix Mechanics
11Eigenvalues and Eigenvectors. DVR Method.
12Matrix Solution of Harmonic Oscillator (Ryan Thom Lectures)
13Creation (a ) and Annihilation (a) Operators
14Perturbation Theory I. Begin Cubic Anharmonic Perturbation.
15Perturbation Theory II. Cubic and Morse Oscillators.
16Perturbation Theory III. Transition Probability. Wavepacket. Degeneracy.
17Perturbation Theory IV. Recurrences. Dephasing. Quasi-Degeneracy. Polyads.
18Variational Method
19Density Matrices I. Initial Non-Eigenstate Preparation, Evolution, Detection.
20Density Matrices II. Quantum Beats. Subsystems and Partial Traces.
III. Central Forces and Angular Momentum
213-D Central Force I. Separation of Radial and Angular Momenta.
223-D Central Force II. Levi-Civita. εijk.
23Angular Momentum Matrix Elements from Commutation Rules
24J-Matrices
25HSO + HZeeman: Coupled vs. Uncoupled Basis Sets
26|JLSMJ>↔ |LMLMS> by Ladders Plus Orthogonality
27Wigner-Eckart Theorem
28Hydrogen Radial Wavefunctions
29Pseudo One-Electron Atoms: Quantum Defect Theory
IV. Many Particle Systems: Atoms, Coupled Oscillators, Periodic Lattice
30Matrix Elements of Many-Electron Wavefunctions
31Matrix Elements of One-Electron, F (i), and Two-Electron, G (i,j) Operators
32Configurations and L-S-J "Terms" (States)
33Many-Electron L-S-J Wavefunctions: L2 and S2 Matrices and Projection Operators
34e2/rij and Slater Sum Rule Method
35Spin Orbit: ζ(N,L,S)↔ζnl
36Holes. Hund's Third Rule. Landé g-Factor via W-E Theorem.
37Infinite 1-D Lattice I
38Infinite 1-D Lattice II. Band Structure. Effective Mass.
39Catch-up
40Wrap-up




 
 


 



 








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