QuTiP VS qmsolve

I think Python would be a more mainstream choice and so you'll find modules like qiskit or [qutip(https://qutip.org/) already exist and will make life easier.

If you want to be a bit more physics-focused in your coding, it might help to dig up a course or textbook on numerical methods in physics. Being able to numerically solve differential equations is probably the most generally applicable skill in physics. Machine learning methods are pretty ''hot right now'' and might be fun to have a look into. And for quantum technology in particular, you might enjoy having a look at some python packages like Kwant for quantum transport, QuTiP for quantum dynamics and Qiskit for quantum computing. You won't understand the physics for this for quite some time, they might help serve as a bit of inspiration and an indication as to what physicists can use programming for.

If you're talking about simulating a hamiltonian on a regular computer then you may want to check out Qutip. It's a python module where a lot of this stuff has already been worked out, including simulating time dependent hamiltonians. I did an undergrad project on QC and this helped me get past a lot of the roadblocks like this and freed up more time to learn about the field, it also becomes a useful toy to play around with and get an intuition for a lot of stuff.

Very nice. I just stumbled upon this repo in my free time that I was going to take a look at https://github.com/quantum-visualizations/qmsolve. Also does visualization of Schrodinger’s eqn

In the visualization, the color hue shows the phase of the wave function of the electron ψ(x,y, t), while the opacity shows the amplitude. The transmittance spectrum, computed by taking the Fourier transform of the incident and transmitted wavefunction, can be found in this plot.

The simulation was done with qmsolve, a python open-source page we made for visualizing and solving the Schrödinger equation.

As mentioned in another comment, here's the link to the source code. For the split-step method I found this resource very helpful. For the Crank-Nicholson method I don't have any free resources to share, except for the wikipedia article. There is another method from this article which is easier to implement than split-step or Crank-Nicholson since it doesn't require taking Fourier transforms or solving a system of equations. You may find the stability conditions to be too limiting when it comes to performance, at least when compared to the other methods.

The simulator used can be found here.

The Schrödinger equation was solved using a Split Fourier method, which is one of the most efficient and accurate methods to solve the time-dependent version. The simulator used is also OC and is posted here.

Also, the script that returns this visualization can be found here.