What does the second derivative actually do in math and physics?

Happy Quantum Day! :) In this video we discover how we can understand the second derivative geometrically, and we derive a few physical relations using this intuition.

Animations:
All animations created by me within Python, using Manim. To learn more about Manim and to support the community, visit here:

Music:
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♪ Intro by HOME
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[quantumsensechannel]

Hi everyone! A quick note:

At 7:55 and onwards, there should be a vector sign over the input of the function: f(vector{x}), since now whenever we are talking about 3 dimensions, the input to the function is a coordinate in 3D space. Apologies for any mild confusion!

I remember I used to dislike when my professors would lazily forget to write vector symbols — but years later it seems I have become what I once despised, whoops.

Hope you all enjoyed the video!

-QuantumSense

[charlie_]

I never understood why there was all this talk in my classes about the second derivative/laplacian being related to an average value, but no actual calculation/explanation was ever provided. Thank you so much for doing god’s work! 🙏

[krupt]

LET'S GO DUDE. I got an 9/10 in quantum mechanics I thanks to you

[unebonnevie]

In college/university, professors/TAs regurgitate a lot without much explanation! Thank God there is YouTube and channels like this!

[arunsevakule]

This is one of the finest educational videos I've ever come across! Please never stop making them!!

[scarlet]

free education for a guy like me who can't pursue physics due to the conflict in Manipur and now here in hyderabad getting a free education for ba course hahaha

[VegaOfficiaI]

You're content has really motivated into learning more about quantum mechanics and physics. Keep doing what you're doing!

[sumedh-girish]

You're back!

Edit: Changed the course of history from talking about his back, to the fact that he is back. You are welcome.

[bobross]

I think that Feynmann was talking about the Cauchy integral theorem. He stated he didn't need to know the center value just the value on the exterior ball.. that is exactly the Cauchy integral theorem -- you average the surface of the ball and you have the center value

[jacoblampmatthiessen]

Thank you! For this very clear and intuitive explanation.

This view really helps seeing the very deep philosophical connection to notions and axioms of locality in mathematical models. And it also makes the connections between wave equations and continuity equations very intuitive! ❤

[LucasVieira-obfx]

I've already read about how Laplacian can be interpreted as the difference between a point and the average of its vicinity, but your visuals nicely complement that picture. Nice work!

[MrFtriana]

Great! The Schrödinger equation is postulated in many texts and one form to derivate it is using the path integral formalism, but you give a good argument about why it have the form that we know.

[TheFireBrozTFB]

As a physics major, you are carrying my ass through QM and modern physics.

Cheers! You’re amazing!!

[vikrantsingh]

really glad you returned, i was really fed by watching your videos on repeat, finally some new content

[TheYoutubeFreak]

Hi, I found your channel just yesterday. I did check out all your videos. I don't know how to express my love and respect towards you. I'm an undergrad student from Bangladesh. I am really interested in quantum computing. I want to learn more. And your channel seems to be a great resource for people like me. Keep up good work.

[pekorasfuturehusband]

YOU’RE BACK!!! This is what we’ve all been waiting for, welcome back king 🙏🏻

[logician]

Excelent video, it really gave me a new perspective on the second derivative. I wonder why the third, and other higher order derivatives are so rare in physics compared to the first and second...

[sarveshpadav]

The video content was quite insightful! Thanks for the upload. I hope you'll continue to do so in the future.

[ajejebrazor]

Thank you! What a great video! Multiple insights and new visualisations.

[viktorvegh]

We need more channels like this! Subscribed