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First class on the WKB approximation

1) Discussed the Heisenberg equation of motion applied to the simple harmonic oscillator 2) Discussed coherent states

Finished going through the Green's function slides and started looking at path integrals.

Introduced the propagator and began slides on Green's functions

Discussed how to include electromagnetic fields in the Schrodinger equation and path integrals, and also covered the Aharonov-Bohm effect

Showed how to find transition amplitudes from the Dyson series. Began analyzing 1st order perturbations constant in time except for being switched on at t=t0.

Introduced the interaction picture

Wigner-Eckart theorem. Note: I previously thought I had lost the recording for PHYSICS739_AngularMomentum6, but I think I found it (it is on macvideo)

I thought this lecture was lost but I found it!

Looked at general case of adding two angular momenta j1 and j2, and introduced the recursion method.

Started studying the addition of angular momentum using the lowering operator method. Introduced direct sums and direct products of Hilbert spaces for the coupled and uncoupled bases, respectively.

Completed Euler angles, started considering rotation operators for general values of j.

Group theory of rotations: SO(3) versus SU(2). Started Euler angles.

Discussed how to obtain the WKB connection formulae using both the transitional approximation and the complex method. Also applied the WKB method to quantize wave functions in various potential wells.

We calculated the propagator for the simple harmonic oscillator using the Feynman path integral approach.

Finished off this part of the course by looking at harmonic perturbations and also 2nd order time-dependent perturbation theory. Started some slides on ``What is a spin?''

Generalized our treatment of first order transitions to include a slow switch on of the perturbation.

Started perturbation theory. Gave example of quadratic Stark shift of ground state.

Finished slides on "What is a spin?"

Finished L4IdenticalParticles and started L5IdenticalParticlesExchangeInteraction

Finished phase shifts in scattering (L24ScatteringTheory4_Phase_shifts). End of course!

Finished partial waves and began scattering phase shifts (L24ScatteringTheory4_Phase_shifts)

Finished the Born approximation and started partial waves (L23ScatteringTheory3_Partial_Waves)

Studied Born's approximation (L22ScatteringTheory2_Born_approx). Got up to the Yukawa potential.