Brief summary of lectures | |
|---|---|
| Gas. Ch. 14 | |
| Lecture 1: Mon, Jan 12, 1998 |
Introduction, discussion of syllabus. Review of quantum 1. |
| Lecture 2: Wed, Jan 14, 1998 |
Finish review of 3220: angular momentum, and matrices. Eigenvalues and eigenvectors of matrix equations. Introduce the idea of "matrix mechanics". |
| Lecture 3: Fri, Jan 16, 1998 |
Conversion of "Schrodinger wave mechanics" to "Heisenberg matrix mechanics". Operators as matrices. Examples from harmonic oscillator, and (set up) angular momentum. |
| Mon, Jan 19, 1998 |
(No lecture, MLK day) |
| Lecture 4: Wed, Jan 21, 1998 |
Angular momentum as a matrix. Lz, raising and lowering operators, for l=1. Introduction to spin. Spin 1/2 matrices, Pauli matrices. |
| Lecture 5: Fri, Jan 23, 1998 |
Eigenvalues and vectors of spin, in x, y, and z directions. Notation and interpretation of arbitary spinors (in Sz basis) The expansion theorem for spinors. (Intro to Stern-Gerlach) |
| Lecture 6: Mon, Jan 26, 1998 |
Magnetic fields, magnetic moments, spin precession. g factor of electron. Intro to Stern Gerlach. |
| Quote of the day: | It was a little over fifty years ago that George Uhlenbeck and I introduced the concept of spin... It is therefore not surprising that most young physicists do not know that spin had to be introduced. They think that it was revealed in Genesis, or perhaps postulated by Sir Isaac Newton, which most young physicists consider to about simultaneous. Samuel Goudsmit, address to the American Physical Society, Feb. '76. |
| Lecture 7: Wed, Jan 28, 1998 |
More on S-G: decomposition of states, the uncertainty principle, Copenhagen interpretation. Intro to paramagnetic resonance - semiclassical discussion. |
| Lecture 8: Fri, Jan 30, 1998 |
Paramagnetic resonance - formalism (setup) and results. Discussion of more general 2 state systems. Wrap up Ch. 14. |
| Gas. Ch. 15 | |
| Lecture 9: Mon, Feb 02, 1998 |
System of two spin 1/2 objects. Total angular momentum operators, adding spin. Singlets and triplets. |
| Lecture 10: Wed, Feb 04, 1998 |
S^2 operator and the dot product S1.S2. Different bases for "microscopic" or "total" states. |
| Lecture 11: Fri, Feb 06, 1998 |
Addition of more general angular momenta. Introduction to Clebsh Gordon coefficients. |
| Lecture 12: Mon, Feb 09, 1998 |
Examples with Clebsh Gordon coefficients. |
| Lecture 13: Wed, Feb 11, 1998 |
Discussion of angular momentum, more examples with Clebsh Gordon coefficients. |
| Lecture 14: Fri, Feb 13, 1998 |
Parity and exchange/identical particles. |
| Lecture 15: Mon, Feb 16, 1998 |
Example of Parity and exchange/identical particles - intrinsic parity. Brief intro to perturbation theory. |
| Lecture 16: Wed, Feb 18, 1998 |
Answer questions/review for exam. (+ More intro to pert th) |
| Gas. Ch. 16 | |
| Lecture 17: Fri, Feb 20, 1998 |
Perturbation theory. Examples, first order PT |
| Lecture 18: Mon, Feb 23, 1998 |
1st order corrections to wavefunctions, and 2nd order perturbation theory for energy. (More examples) |
| Lecture 19: Wed, Feb 25, 1998 |
Example of 1st and 2nd order pt (Harmonic oscillator in E field) Intro to degenerate perturbation theory. |
| Lecture 20: Fri, Feb 27, 1998 |
Degenerate perturbation theory. Formalism, handy theorem (which allows us to avoid deg. p.t.) and an example (hydrogen ground state in magnetic field) |
| Lecture 21: Mon, Mar 2, 1998 |
Stark effect: hydrogen in E field. Discussion of 1st and 2nd order P.T. on ground state. Calculation of polarizability of hydrogen. Setup (but not solution) of 1st order degenerate p.t. for n=2 levels. |
| Lecture 22: Wed, Mar 4, 1998 |
Stark effect: degenerate p.t. Calculation and discussion of n=2. Discussion of "analytic series" (starts to converge, but ultimately diverges). |
| Gas. Ch. 17 | |
| Lecture 23: Fri, Mar 6, 1998 |
Unit analysis for perturbation theory. Introduction to real hydrogen atom. Relativity and fine structure. |
| Lecture 24: Mon, Mar 9, 1998 |
Finish relativity correction, discuss spin orbit coupling in hydrogen. |
| Lecture 25: Wed, Mar 11, 1998 |
Combined spin orbit and relativity - fine structure of hydrogen. |
| Lecture 26: Fri, Mar 13, 1998 |
Zeeman effect, weak and strong field cases. |
| Lecture 27: Mon, Mar 16, 1998 |
Hyperfine effect, 21 cm line. |
| Gas. Ch. 18 | |
| Lecture 28: Wed, Mar 18, 1998 |
Intro to Helium. Ignore electron repulsion, and solve exactly. Discuss spectrum, and spin structure: degeneracy and Pauli. Electron repulsion as a perturbation. |
| Lecture 29: Fri, Mar 20, 1998 |
EPR and Bell's inequality. |
| Spring break | |
| Lecture 30: Mon, Mar 30, 1998 |
Helium - effective spin orbit splitting, ortho vs para helium. |
| Lecture 31: Wed, Apr 1, 1998 |
Intro to variational method, + exam questions. |
| Lecture 32: Fri, Apr 3, 1998 |
More variational examples (1D), and then the Helium atom solution via variational method. |
| Gas Ch. 20 | |
| Lecture 33: Mon, Apr 6, 1998 |
Finish Helium, look at numbers (discuss ways to improve it.) Introduce molecules, set up H2+ problem. |
| Lecture 34: Wed, Apr 8, 1998 |
Continue with H2+ problem. Discuss molecular vibrations. |
| (Gas Ch. 19 ) | |
| Lecture 35: Fri , Apr 10, 1998 |
Finished H2+ with discussion of rotations. Atoms and period table. (Carbon, as example) Quick intro to combining E+M with quantum. |
| Gas Ch. 13 | |
| Lecture 36: Mon, Apr 13, 1998 |
Maxwell's equations, gauge invariance, and the quantum Hamiltonian for a charge in E and B fields. |
| Lecture 37 Wed, Apr 15, 1998 |
More on gauge invariance, and the quantum Hamiltonian for a charge in E and B fields. (Example) |
| Lecture 38 Fri, Apr 17, 1998 |
Aharonov-Bohm effect, and introduction to time dependent perturbation theory. |
| Gas Ch. 21 | |
| Lecture 39 Mon, Apr 20, 1998 |
Time dependent perturbation theory - formalism. |
| Lecture 40 Wed, Apr 22, 1998 |
TDPT - some applications and examples. |
| Lecture 41 Fri, Apr 24, 1998 |
Sinusoidal time dependent perturbations, Fermi's Golden Rule. |
| Lecture 42 Mon, Apr 27, 1998 |
"A" field corresponding to EM radiation, QED, intro to phase space. |
| Lecture 43 Wed, Apr 29, 1998 |
Phase space, application of Fermi's Golden Rule to radiation of hydrogen atom.. |
| Lecture 44 Fri, May 1, 1998 |
Radiation of hydrogen atom, selection rules, lifetime. |
| Lecture 45 Mon, May 4, 1998 |
Odds and ends, finish up hydrogen radiation, and selection rules. Questions for exam. |
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