Eigenstates of ANY 1D Potential in PYTHON 

You sir, you are a freaking beast! Keep it up and I'll be here every single time!

So awesome! Watching your Python videos is just so immensely intellectually satisfying, inspiring, and galvanizing. Love your videos. The value of your videos cannot be overstated.

This is an absurdly cool video! I have two RU-vid accounts and went on both to like this video. Thanks for the great content. You're fantastic at explaining things.

this video was really clear and fun, and i love how excited you get. thanks for this!

This just became my favourite youtube channel!

When done in discrete form like this it reminds me of solving a system of lots of masses connected by springs. You get an almost identical tradiagonal matrix

This is pure gold!

Road to Reality in the Background. You know the good stuff ! !

This is ridiculously high-quality content

Reminds me of the finite difference method that i used once to simulate a 2D Situation with the Navier Stokes Equations.

omg this is awesome thanks a lot!

Great tutorial, thanks...

素晴らしいビデオです！

Dude, I saw your video about the skydiving differential equation on reddit and was like "meeeh, not again, we don't need this another time". But this, this was brilliant! Great video, nice explanation of a scary problem. Keep it up. Could you also share the jupyter notebooks in the end? Also, I miss the link to your blog in the video description ;) Keep promoting yourself.

YOU are a great teacher (from a professor).

Wonderful content 🔥

Really Great Video! Maybe next time you could compare your results with the analytical ones so in this case the qm harmonic oscillator model. I did it and the results are really close! So again thanks for the video

Life saviour ❤️

Hi Luke, Just a courtesy to let you know that I cited this video in a recent paper. Can't put any details because it gets deleted for containing a link but you can probably find them in your comments box. Great channel!

You are awesome too good

I was trying to solve woods-saxon potential. I was messed up myself by numerov's algorithm. Then I found your video. Finally I solved the problem using this tridiagonal eigenvalues. But I want to make a request. Can you make a video on how to find all the eigenvalues in a certain range, for any 1-d potential using numerov's algorithm and shooting method.

that was so cool! saving this. can you show how to do that for the 3D equation? Also can you explain the way you wrote the d variable in your code?

Really enojoy this type of content, a good way in my optinion to learn Python if you know some physics

damm looks similar to the euler lagrange equations we studied in aeroelasticity

Hi, amazing video. I wold like to ask I tried to model hydrogen atom with potential in a form of 1000/y, the problem of dividing by zero I solved by starting at y=0.0001 and since energy is not 0 at the right end- in infinity I extended the matrix by one element. The wavefunction looks quit similar to the hydrogen atom but I am not able to see the "infinity" in the graph even if I set N to 10000. Any suggestions will be highly appreciated, have a nice day.

how does this extend for the case of a 2 dimensional schrodinger equation?

very nice video! I have a lot of fun using python again! One little question, maybe it is a conventional thing. Then you divide by Δy^2, do you actually mean (Δy)^2 ? (since it is the 2nd (discrete) derivative?

Can you make your seriers of videos as in a particular playlist? Or anyway to group some of your videos, so that we can play all vidoes in a list ? ^_^

MAKE DIRAC EQUATION

I have liked and subscribed. Please show me how to make a chemistry simulator. I want the orbitals to dance

very interesting. I have one simple doubt about the number of eigen states. The number of eigen states is equal to the dimension of the matrix, and the dimension of the matrix depends on the number of points we have chosen. So, the number of eigen states depends on the method of solutions!?

However you can't use this method for scattering states, as you can't set the boundary conditions as psi(0)=psi(L)=0.

What happened to reduced planck constant in the non dimensionalization step?

Can I get the link for the Wordpress paper ?

This is similar to the problem 2.61 of Griffiths 3rd Edition

Does it work for a non-linear potential that depends on Psi (my example is: Laplacian of V = - Psi^2) ?

16:20 aren't energy levels in sho supposed to be equally spaced? In there m and L both are constants so your bar should be increasing linearly right? It seems a little off

How would one solve for energies if the wavefunction is leaking instead of being zero at 0 and L?

Hi, it is interesting video. learn a lot from it. but there is a question about the demensionless step. in term of potenial, why directly become mL^2V(y)phi? why not mL^2V(Ly)phi?

Hello. I've got one doubt. The energy output is quadratic. I think that it would be linear, since E = (n + 1/2)hw? Am I wrong?

Sir,can you post the code here

Why V(x) = L^2V(y)? What if the V(x) = x^4 or something else...?

There is one thing that I do not understand. psi(x) is a complex number, but according to this video, it seems to be always real number?

137th like

Literally smarter than that guy on your wall

A very small tip. The topics you're representing are good and cool and all that. But I didn't learn them this way. Your videos aren't educational if that's what you want them to be. They are more like "look I can do cool stuff, and you know what, just take the code from the description, because I know that you can't do it yourself". Try to focus on the problem and discribe the code slowly. At the end we both KNOW, that these problems aren't a big deal. Peace.