Hi everyone! 👋

I’m passionate about quantum physics and software development, and I’ve been consuming content on these topics for quite some time.

This curiosity led me to create a personal project: Genesis, a simulator that calculates atomic and subatomic physics in real-time on PC.

If anyone would like to test the simulator or discuss it, you can find it here: https://genesis.gemmi-e.com

Gotta love it!

This post begins with the foundations of mathematical physics for students learning quantum mechanical angular momentum for the first time.
I believe that providing a more detailed mathematical approach over one or two additional pages can offer hope to a broader range of learners.
I have organized these notes to strip away the shell of complex symbols using the language of linear algebra, aiming to translate the underlying physical reality into a level of common sense that anyone can understand.
Good luck!

One pattern I've noticed among enthusiasts is that they're really excited about QM but lack the time and/or math to actually learn it. There's no shame in this, but some people in the physics community say that real learning can be done by working with concepts only. This is good in principle, but I'm unconvinced that it actually works. In order to teach with concepts only, you have to move from the domain of math (the only actual domain we understand QM in—see foundations for more on that) and move into the domain of metaphor and allegory. This carries a great deal of risk for the student. I've found that beginners who are interested in this conceptual domain often internalize QM in this language of metaphors and get it slightly (or very) wrong. They can become confident in an understanding that is seemingly correct at the surface but horribly wrong when probed for actual understanding. This may do more harm than good.

That's not to say the correct response to curious beginners is to shut down their interest. That would not be ideal at all. But I would say it's important to emphasize that the no-math conceptual approach is no substitute for mathematical experience and that they cannot hope to actually understand QM until they've done the math. The standard beginner concepts serve as enticing slivers of the actual pie that do very little by themselves but might beckon the student a step further into the quantum world.

I would say that, in my experience, conceptual learning only begins to reveal the shape of understanding once a student is comfortable with linear algebra—particularly vector spaces. You do not need to solve the TDSE to be able to understand, but you need some way to grasp that English is the map and math is the territory. There is no deeper territory beneath that as there is for classical physics. (By territory I mean what a physicist means when they say they understand QM).

I understand that this is essentially calling for more gatekeeping, but I don't think it is without good cause. Gatekeeping is not a position I have deep conviction for, but more of a hypothesis I wanted to get some thoughts on from physicists beyond myself. What do you guys think?