Comment on Observer
cynar@lemmy.world 1 week agoWhile 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.
andros_rex@lemmy.world 1 week ago
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.
someacnt@sh.itjust.works 1 week ago
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?
andros_rex@lemmy.world 1 week ago
Eigenvalues come from linear algebra. I think a difficult think in general with understanding them is often the failure of most middle/high school math teachers to teach matrix operations at all. (I’m guessing because matrix multiplication never shows up on SAT/ACT). Here’s a good explanation for the math on finding eigenvalues and eigenvectors.
But basically eigenvalues are going to be associated with certain matrixes/vectors. You take a “Hamiltonian” of a system, which is a way of describing possible energy values in the system, and it’ll give you a set of possible answers - pairs of eigenvalues and eigenvectors that describe the system.
In effect - you get things like the quantum numbers. That the 1st energy level has 1 subshell can hold 2 electrons, both with opposing spins. That the 2nd energy level has a 2s subshell that holds two, that 2p holds six. You get your n (1st energy level, 2nd so on as you go down periods of the periodicity table), l (subshell - don’t get a SPeeDy F), m (which breaks down where in the subshell they are) and the need for opposing spins.
someacnt@sh.itjust.works 1 week ago
Thank you for in-depth explanation! Though I already know the eigenvalues and eigenvectors, as a math major. What I am curious of is: why can’t we only observe e.g. energy values? I heard that one can only observe commutative operators or something, but honestly why is quite unclear.