Agemoz's Physics Blog

I’ve put a lot of fixes and user interface controls into my differential equation solver, and tested it with a number of Schroedinger equation homework problems from my physics classes, and getting matching results. I so badly wish I had done this while taking my classes–I can analyze so many internal variables and visually see how different Hamiltonians and energies affect the solutions. I can tweak the energies and the eigenstates just pop out! Any energy that is not an eigenstate results in unbounded psi (see pictures), so in real time, I change the Hamiltonian energy component up or down and watch how psi evolves and watch for the eigenstate values as I pass by them.

This differential solver is still very basic, only one dimensional, but it is very clear in my mind that this will be extensible to 2 and 3 dimensional solutions–at which time, I’ll start testing the u,d,u charge and spin solutions I hypothesized in previous posts.

This is so fun and amazing. In class, I learned many sophisticated mathematical tricks to get answers to simple differential equations, but also learned that the vast majority cannot be solved and require simplifying assumptions just to get an approximated solution or a range of possibilities. I confess that I didn’t really enjoy that approach to physics–it was so laborious and so limited, and I really felt like that methodology wasn’t really sustainable or scalable at all. Using a computer with applications like this differential solver feels unbounded in its potential to make headway and I have visions of exciting paths to discovery and learning that I rarely got from class. This is why I love and am so energized by physics!

Agemoz

Tags: physics, quantum, special relativity

This entry was posted on July 22, 2022 at 5:31 pm and is filed under Physics. You can follow any responses to this entry through the RSS 2.0 feed. You can skip to the end and leave a response. Pinging is currently not allowed.