@6:00 there is a big problem. While psi might go to zero at -inf and inf, x itself goes to infinity. You didn't address how the product is zero. How do you know psi goes to zero fast enough to cancel the effect of x going to infinity so that the resulting product is zero. Pretty big problem with physicists trying to do math. They manipulate symbols according to their whims. There definitely is a rigorous way to do it but its sad that in many of the lectures (even in textbooks like Griffiths), they pull a rug over it.

Dear Dr., thanks for the great lecture. Please allow me for one question. So your example total N=4, what if we increase N to 8, double the data points, 1) does delta_x change or do you use fixed domain range? 2) we can still keep k=1,2,3,4 for f_hat or we have to increase k to 8 as well? 3) does that change the results? Thank you very much for your advice!

Where does the sin of theta come from for dA?

wow!

Thank you

Great, compact, understandable. Thank you!

Best mathematically rigorous, yet accessible introduction to spherical harmonics i've seen on youtube. Thank you

Thank you sir!

Excellent video!

Yeah I’m learning that in year 5 and this video helps

Can you give examples of how it can operate with matrices?

amazing

Nice

Thanks so much I missed a few weeks of school this semester and my physics teacher is being very unhelpful. This helped me very much on my unit project!

I am a certified professor and princeton and realized the immediate mistake at the beginning of the video. You noted both the -infinity and infinity on the integral symbol, which is completely unneccessary.

This makes sense thank you!

Oh wonderful! Wonderful! Thank you!

That gif in the lower-left from 1:15-1:25 helped so much. It was hard to visualize before that. Thank you!

You sir, have been a huge help. Many thanks!

So clearly explained thank you man! Makes sense.

Thanks a lot! But.. can anyone tell me where does this original differential equation come from? Why would anyone even try to solve this in 17xx? It feels like it just appears out of thin air, and then like - btw let's use it to solve Schrodinger equation...

lambda=0 ends up being a trivial answer that not fulfill the boundary conditions, but lambda>0 has non trivial solutions (and that fulfill the boundary conditions)?

truly my lifesaver, thanks a lot sir

Need explanation of the maths.

Sir, its "infinitesimal" and not "infintesimal".

Your review is very good, but i have no clue whats going on here, im just high as hell 🤣

Genuinely good video

Hello sir,Could u pls help me to know in case of complex eigen value with with negative real part we have trajectories in the form of decaying spiral but how to know they are clockwise or anticlockwise

I've been SCOURING for a concise and clear tutorial and finally found one!! Dr Underwood, thank you so much for saving this physics undergrad this many years later. Cheers!

Hi Sir, your explanation is very clear and understandable. Thank you.

why is Y(y) not a complex function? From my class notes, is k^2 is negative it's sin+cos, but if it's positive then the solution to the de is a function of sinh(ix) + cos(ix)

Excellent. Thanks for making these videos available.

hi from IZTECH xd

The best explanation I found on youtube in 3 hours. Thank you very much!

notations confusing gosh.

thank you very much! <3

Smart comparison between Dirac and shrodenger QM

uses feet and inches. Can't take this series. Next video

Last video cliff hangered me so hard

Very good thanks alot mr

Thanks you verry much!

How can we import sound waves data into sagemath

What's that program you used at the end to plot the graph?

How do you check the solution at 7:48 ?

most clear explanation on this

Simple and clear explanation!

Awesome content bro thanks

Unbelievable video so helpful

After watching this and other mathematical videos, I know that mathematics equations needs memorizing and if you don't, you'll fail

Can u explain how can we find the da in here I'm confused thank u .