Quantum Tunneling: Explained and Modeled with Numpy Python

Here's how to build a model for a particle with quantum tunneling using python numpy and the finite difference method.

00:00 - Intro
01:07 - Theory
02:27 - Finite Difference Method
04:57 - Eigenvalue problem
07:18 - Superposition of eigenstates
10:36 - Python setup
15:27 - Creating potential
17:18 - Creating initial wave function
20:39 - Creating Hamiltonian matrix
22:22 - Eigenvalues and eigen vectors
25:51 - Finding c coefficients
28:03 - Finding Psi(x,t) and simple animation
32:13 - VPython animation

Here is the code:

Here is the cheat sheet (I forgot to include it at the end)

[dushyantkumar]

It was truly a joy to see a straightforward translation of quantum mechanics into code without any convoluted and non-intuitive steps.

[albertmillimono]

God Bless you Sir for making this so understandable for me! I struggled in my whole student life to understand logic of physics programming and here I got something!
Thank you

[fizixx]

In case anyone wants to know, this will work in a platform like Pycharm, and I imagine Spyder also, but the plot opens in your default browser. The barrier in the square-well is it. Will be playing with this one for a while. Thank you

[rugvedzagade]

Two part question
a) how did you find the initial wave function and what exactly is Cn
b)while normalizing psi0 we didint take account of i in the second exponent ?

[tayyabali]

This problem represents a potential barrier in quantum mechnics. In barrier case, the solution should be wave like outside the barrier and frozen(exponantial) inside the barrier. In this animation i have seen that the solution is wave like inside the barrier, which can't be. Why is so ?

[marcrindermann]

if anyone is interested watching this, when your cell is markdown, rather than copying and pasting your code into a code cell, you can just change your markdown cell back to a code cell.

[rugvedzagade]

How did the normaliztion of psi0 worked for all the psi's

[shashankpandey]

THANK YOU FOR THE AMAZING LECTURE PROFESSOR.I have doubt at time stamp 38:33 why the wavefunction inside the potential barrier is not exponentially decaying?

[misterx]

How did you program the envelope of the wave in the teaser animation at the beginning of this video?

[alexanderlomashvili]

Is there a sign error for the Hamiltonian at timestamp of approximately 22 minute mark? The variable H has the wrong sign, I am pretty sure, when compared with the sign used for the lecture slides at timestamp of approximately 6 minutes mark.