What A Path Integral Problem Looks Like In Quantum Mechanics

I've been working on my homework for quantum field theory, and thought maybe it be cool to show what these path integral problems actually look like.

[zamoradecesare]

This looks so exciting and interesting, i can’t wait to get to a point where i understand this properly

[oscarobioha]

Wooow.
Beautiful...i dont understand but still....its beautiful

[SomewhereGalaxy]

I’d love to see more videos of you getting us more involved with the problems you’re solving and potentially even showing solved solutions, great video man!

[Adamrpg]

The path integral approach allows for better motivation for certain approximation schemes (like mean field theory) and seems better suited for when you consider your particles to be bosons/fermions. You'll have lots of fun working with Grassmann variables, I bet a couple of videos will come out of that!

[TheZod]

I'm in first year E&M so nothing you says is tangible to my mind and yet it sounds so cool.

[lukesaunders]

Just started my advanced QFT course this week! We’re building up to the path integral at the moment, starting with functional derivatives/integrals etc. (not everyone will have done those). I’m hoping I can still be convinced QFT is fun. Path integrals to my knowledge are super useful for Non-Abelian Gauge theory. It’s a shame that they are mathematically questionable...

[philliesphan]

What program do you personally use for latex?

[pennrogers]

I mentioned this on a previous video, but you should check out Feynman and Hibbs book Quantum Mechanics and Path Integrals for a tie to thermo & stat mech. The first chapter also provides the intuition behind the path integral.

[aliobeid]

carry on please! go as deep as possible in the meaning of the mathematics used

[charliesuarez]

Don’t hold back. Drop all them sexy-ass equations on top of us.

[Ridwan-wmis]

First. Nobody said it, so I did. Please gimme a heart sticker. I’m on the way to school so I’ll watch this when I get home. Damn I hate time zones.

[konstantinospapafilakis]

How can one derive the wavefunction via path integral? Please answer me analytically.

[qingyangzhang]

It looks so cool and it intimidates me at the same time. But I really hope that I can understand this one day

[RockieAtlas]

This looks like the most complicated thing I have ever seen. It looks cool but I have no idea what any of it means😢😂

[konstantinospapafilakis]

I am looking for path integral examples for a long long time but I cannot find how one derives the propagator for a free particle via this Integral. Can you propose the solution or at least give me some useful information? I need this

[konstantinospapafilakis]

What textbook do you use at your university?

[CalculusPhysics]

Being a first year physics student, this looks lowkey terrifying and i only understood the Fourier Transform and the Lagrangian parts, BUT i’m hopeful that i’ll eventually learn how to approach stuff like this!

[bilalhussein]

For non-relativistic quantum mechanics path integrals aren't very useful but when you try to quantize a relativistic particle you are forced into a field description.

From there the concept of the effective action and renormalization group get you a great deal of QFT. Path integrals are the most natural and easily generalizable way to do QFT. While offshoots of the idea like Wilson loops appear in heavy duty mathematics like knot invariants, the topology of both three and four manifolds, and counting the intersection of curves on moduli spaces. Pretty much everything Witten's done since the mid 80s and has lead to at least three Fields Medals.

[whalep]

I believe a Laplace transform reduces ODEs to algebra whereas a Fourier transform reduces PDEs to ODEs.

[charredmars]

Did Andrew take one of my suggestions and use it in a video? I'm so honored even though I probably wasn't the first to comment it. :p Great video, Andrew. :)