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this post was submitted on 23 Feb 2025
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Tbh, I think no one who hasn’t solved the Schrödinger equation at least once (at least time independent), should be allowed to talk about quantum.
Like, the uncertainty principle is really really fucking cool when you understand why it works mathematically. But without differential equations and linear algebra, I don’t think it’s possible to really conceptualize what’s going on in quantum.
Idk, I always try to explain to students the deficiencies of the Bohr model and explain the significance of the electron cloud, but probability is hard.
One of my favorite things in quantum was deriving the “quantum numbers” they have you memorize in chemistry (if you don’t remember, you probably got a SPeeDy F) It’s beautiful to watch the way they emerge from the second order diff eq.
While I'm rusty as hell, my physics degree was actually focused quite a lot into QM.
It's perfectly possible to get a reasonable understanding of what's going on without going head first into the maths. There are definitely areas however that we don't have a good conceptual model of yet. For those, the maths definitely leads the way. 90% of QM is comprehendible with relatively little maths. You only need the maths when you start to get predictive.
I don’t think you can get the intuitive feel/the “why” without the maths.
I guess I get frustrated when I have to teach algebra based introductory physics for similar reasons - everything makes so much more sense when you understand how the pieces fit together. (Why make them memorize d=d0+v0t+1/2at^2 when all that is integrating a constant twice? That you can set v=0 to find the time of maximum height, because you’re using a derivative to find a max! And then that helps you get why it works, and then even how to possibly explore non constant acceleration!)
I got really fucked over because I didn’t take linear (at all - advising in my physics department was non existent which lead to things like taking classical before Diff Eq lol) and so things like eigenvalues - which tbh I think is kinda the money shot - that things end up quantized and discrete - that took a while for me to get what that meant.
I find QM quite confusing, in that one can observe only the eigenvalues and not the state itself. Why is it specifically, or is this wrong conceptualization? Also, how does particle-ness relate to the eigenvalues?