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
Пікірлер: 9
WE NEED MORE OF THIS CONTENT!! You must become famous instantly in science youtube
Wow this series is actually still updating... Thank you so much for doing all these, extremely clear and helpful!
PLz put this video and video 8 in the optics playlist! Thanks for the contect!
This explanation is excellent!!!
In the non-relativistic “Feynman all path propagation” formalism an existing infinite spacetime is assumed (∆x=±∞,∆t→0). Using all causal paths will solve the need for an non existing infinite spacetime.
Please show us the Damped quantum harmonic oscillator and the master equations
@ 03:02 The comparison is a bit unfortunate. A classical wave function describes something physical, while the quantum mechanical wave function has no physical meaning. It's just a mathematical tool. @ 12:40 This picture (on the right) is NOT correct. No photon travels back in time. You should have used the picture on the left and changed the z-axis into a time-axis. Then, we're doing physics again. Read about "time-slicing", Sander.
The name Snell (with double L) is an anglicisation of the Dutch name Snel (with single L). Anglicisation is like colonisation. You want to impose your own culture on everything :-(