Solving Schrödinger's Equation as an Eigenvalue Problem with Numpy

Solving the 1D infinite square well using the finite difference method and the eigenvalue problem. In this example, I'm using python numpy

Here is another finite difference method using lists

Here is my analytical solution to the 1D infinite square well.

After that, I created a numerical solution in python using the shooting method.

[sbaidya]

Thanks for such a nice tutorial of the subject. I am just curious if it is possible to plot eigenstate in python in 3D.

[moirangthemsanahal]

i dint understand why did we transpose the psi. The psi array was giving the different eigenvectors as sub-arrays right? then our interest is that very subarray only right? why then transpose? or may be i dont understand the output itself

[rugvedzagade]

Why did we normalize? We could just square psi2 itself and plot it

[KristineDzneladze]

why are we transposing psi? what is physics and mathematics behind it?

[SampleroftheMultiverse]

U Shape Wave


Thanks for your informative and well produced video.

You and your viewers might find my quantum-like analog interesting and or useful.

I have been trying to describe the “U” shape wave that is produced in my amateur science mechanical model in the video linked below.

I hear if you over-lap wave together using Fournier Transforms, it may make a “U” shape or square wave. Can this be correct representation Feynman Path Integrals?

In the model, “U” shape waves are produced as the loading increases and just before the wave-like function shifts to the next higher energy level.

Your viewers might be interested in seeing the load verse deflection graph in white paper found elsewhere on my YouTube channel.

Actually replicating it with a sheet of clear folder plastic and tape and seeing it first hand is worth the effort.