Classical physics derived from quantum mechanics: Feynman Path Integral

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Classical Mechanics and Relativity: Lecture 5
0:00 Introduction
2:35 Fermat's Principle
9:57 Variational principles
17:16 Double slit experiment
21:38 Quantum interference
25:08 Feynman Path Integral
31:12 Quantum trajectories
38:26 Classical Action of quantum paths
42:36 Path integral representation of wavefunction
44:17 Classical path from quantum interference
Theoretical physicist Dr Andrew Mitchell presents an undergraduate lecture course on Classical Mechanics and Relativity at University College Dublin. This is a complete and self-contained course in which everything is derived from scratch.
In this lecture I make the connection between classical mechanics and quantum mechanics. By analogy to Fermat's principle of least time in the theory of optics, and by considering a generalization of the double slit experiment, I introduce Feynman's Path Integral formulation of quantum mechanics. From it, I derive the principle of least action, and hence all of classical mechanics.
Full lecture course playlist: • Classical Mechanics an...
Course textbooks:
"Classical Mechanics" by Goldstein, Safko, and Poole
"Classical Mechanics" by Morin
"Relativity" by Rindler

Пікірлер: 34

@patb3845 8 ай бұрын

the best simple explanation of path integrals I have seen.

@a.c.e7407 Жыл бұрын

Best...explanation...ever. I cannot express how much this helped me in both understanding the math and being able to now understand the more complex formulations with normalization in them. I cannot thank you enough. This video deserves to have at least 10 million views, there is literally no other source that explains it this well. I with all of my being, significant or little, thank you for the time and passion sir.

@jacobvandijk6525 5 ай бұрын

For every explanation there is an audience on KZfaq. For some this is too much, for some it is enough and for some it isn't. So, in your own small world, it deserves more likes ... but that's only in your small world. Remember, a.c.e., you are not the standard for what is best or not. But I know how it feels when you think you understand something for the first time.

@shrd8842 Ай бұрын

Excellent and ground up explanation of Feynman path integral. Thank you.

@iliavarnaseri1840 2 жыл бұрын

I am amazed by how you are able to articulate these complex subjects so clearly! I am loving these lectures!

@stauffap 2 жыл бұрын

I've been looking for this type of mathematical discription of what feynman was talking about in his lectures for a couple of years now, so this is very exciting to me. Now, i can finally tackle some problems quantitatively :) Your explanations were very clear and understandable, thank you!

@schmetterling4477 11 ай бұрын

Feynman's original paper from 1948 is online. Are you telling us that you didn't take the time to read it? ;-)

@irtazaazim3080 3 жыл бұрын

each word you speak is full of wisdom.... loved it

@camac7988 Жыл бұрын

Beautiful lectures, always so clear. Love from italy

@sengseclectictechsharings1085 2 жыл бұрын

excellent explanation!

@shitheadjohnson2797 2 жыл бұрын

THIS IS A GOOD LESSON!!!

@andiware2440 Жыл бұрын

Thank you very much. This was great review on a tricky topic.

@stevenschilizzi4104 Жыл бұрын

Very clear introduction to Feynman’s PI. Many thanks for your effort. This has raised my curiosity, however, and I’m interested to know how one goes from this introductory exposition to the more standard form of FPIs that have an integral in the exponent of e. Could you do a video on that? Thanks again!

@michaelpotter3418 2 ай бұрын

Brilliant explanation! Thank you!

@jeffwyss 8 ай бұрын

Compliments. Very well done.

@gaussdog 3 жыл бұрын

Amazing…love it

@jamesraymond1158 Жыл бұрын

Beautiful!

@joelasaucedo 3 ай бұрын

So good!!!

@realdarthplagueis 3 ай бұрын

Great video! Probably the best explanation I have ever seen of these ideas. I have one (perhaps stupid) question: If the paths around the path of least action creates constructive interference, why can't paths around (very near) other paths do the same? In your example you drew 3 vectors whose sum was nearly zero, and therefore had destructive interference, but would one not see constructive interference for vectors near (similar) any of the individual paths in that example? So I guess I don't understand why the sum of these vectors _around_ the path of least action is so special, given the argument about the sum of the vectors in your example.

@louis4798 2 жыл бұрын

the intensity should be proportional to A^2, but you said it equals to A^2?

@GBY13 2 жыл бұрын

The lecture was very nice, sir. I have a question. Why action S should have the same dimension as phase (precisely, S/ħ)? Is this by coincidence? Or any interpretation?

@a.c.e7407 Жыл бұрын

The action S is a number, so is h, hence why we have S/h in the exponent. If they are not scalars, how would you perform the exponentiation?

@a.c.e7407 Жыл бұрын

Interpretation would be S is like a utility, so it gives a quantitative measure of how good your path is. You would want to have an extremum depending on your problem for the optimal path. Hence why it is a number. And h is a constant so also a number.

@xjuhox 3 жыл бұрын

Nicely done! But the choice of quantum phase, ϕ = kx - ωt, is not an obvious step.

@drmitchellsphysicschannel2955 3 жыл бұрын

Thanks for the question. This relates to the part of the video from 30:00 to 35:00. For a classical wave, A=cos[ϕ] with ϕ=kx-ωt. For a quantum mechanical plane wave, we have A=Exp[iϕ]=cos[ϕ]+isin[ϕ]. So ϕ is simply the phase of a complex plane wave. As explained, any motion over a small enough time step dt can be viewed as being in a straight line, with constant wavelength and velocity, and hence dϕ=kdx-ωdt for that segment. It is basically just a way of parametrizing the complex normalized quantum wavefunction of a particle.

@hershyfishman2929 2 жыл бұрын

25:10 Anthony Zee says he "just" made up this story kzfaq.info/get/bejne/laeKl9mly5zMgIk.html at 36.26 timestamp

@drmitchellsphysicschannel2955 2 жыл бұрын

Thanks for this! The story indeed has an apocryphal feel to it. However it is still very useful in understanding the basic idea of the path integral, which can otherwise seem somewhat mysterious. Also it's a pretty amusing story! So I'll keep it in with the phrase "possibly apocryphal", even though we secretly know it is "definitely apocryphal"!

@patb3845 8 ай бұрын

Fascinating bit of history.