09. Optics and Mechanics (Feynman path integral, Born series, Hamiltonian optics, Wigner function)
0:43 Comparison of quantum mechanics with classical wave mechanics
4:30 Recap of basic quantum mechanics (wave function, position and momentum states, observable operators, Hamiltonian, Schrodinger equation)
7:00 Fermat's principle of least time
9:37 Hamilton's principle of least action
11:19 Wave model: assigning phases to rays/particle trajectories
13:15 Feynman path integrals
15:57 Optical scattering (perturbations, Born series, multiple scattering, Feynman diagrams)
24:05 Euler-Lagrange equation
27:31 Hamiltonian equations of motion
30:10 Phase space
32:00 Comparison Hamiltonian mechanics and Hamiltonian optics
39:00 Time evolution of a classical probability distribution in phase space
43:57 Wigner distribution function
48:03 Heisenberg picture of quantum mechanics
52:47 Comparison classical Hamiltonian mechanics and quantum Heisenberg picture
55:37 Summary
