This calendar provides the lecture topics for the course.
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LEC # |
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TOPICS |
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I. One Dimensional Problems |
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1 |
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Course Outline. Free Particle. Motion? |
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2 |
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Infinite Box, δ(x) Well, δ(x) Barrier |
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3 |
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|Ψ(x,t)|2: Motion, Position, Spreading, Gaussian Wavepacket |
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4 |
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Information Encoded in Ψ(x,t). Stationary Phase. |
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5 |
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Continuum Normalization |
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6 |
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Linear V(x). JWKB Approximation and Quantization. |
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7 |
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JWKB Quantization Condition |
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8 |
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Rydberg-Klein-Rees: V(x) from EvJ |
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9 |
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Numerov-Cooley Method |
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II. Matrix Mechanics |
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10 |
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Matrix Mechanics |
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11 |
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Eigenvalues and Eigenvectors. DVR Method. |
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12 |
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Matrix Solution of Harmonic Oscillator (Ryan Thom Lectures) |
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13 |
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Creation (a† ) and Annihilation (a) Operators |
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14 |
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Perturbation Theory I. Begin Cubic Anharmonic Perturbation. |
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15 |
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Perturbation Theory II. Cubic and Morse Oscillators. |
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16 |
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Perturbation Theory III. Transition Probability. Wavepacket. Degeneracy. |
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17 |
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Perturbation Theory IV. Recurrences. Dephasing. Quasi-Degeneracy. Polyads. |
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18 |
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Variational Method |
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19 |
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Density Matrices I. Initial Non-Eigenstate Preparation, Evolution, Detection. |
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20 |
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Density Matrices II. Quantum Beats. Subsystems and Partial Traces. |
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III. Central Forces and Angular Momentum |
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21 |
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3-D Central Force I. Separation of Radial and Angular Momenta. |
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22 |
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3-D Central Force II. Levi-Civita. εijk. |
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23 |
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Angular Momentum Matrix Elements from Commutation Rules |
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24 |
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J-Matrices |
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25 |
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HSO + HZeeman: Coupled vs. Uncoupled Basis Sets |
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26 |
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|JLSMJ>↔ |LMLMS> by Ladders Plus Orthogonality |
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27 |
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Wigner-Eckart Theorem |
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28 |
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Hydrogen Radial Wavefunctions |
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29 |
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Pseudo One-Electron Atoms: Quantum Defect Theory |
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IV. Many Particle Systems: Atoms, Coupled Oscillators, Periodic Lattice |
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30 |
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Matrix Elements of Many-Electron Wavefunctions |
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31 |
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Matrix Elements of One-Electron, F (i), and Two-Electron, G (i,j) Operators |
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32 |
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Configurations and L-S-J "Terms" (States) |
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33 |
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Many-Electron L-S-J Wavefunctions: L2 and S2 Matrices and Projection Operators |
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34 |
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e2/rij and Slater Sum Rule Method |
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35 |
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Spin Orbit: ζ(N,L,S)↔ζnl |
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36 |
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Holes. Hund's Third Rule. Landé g-Factor via W-E Theorem. |
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37 |
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Infinite 1-D Lattice I |
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38 |
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Infinite 1-D Lattice II. Band Structure. Effective Mass. |
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39 |
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Catch-up |
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40 |
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Wrap-up |
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