/sci/ - Science & Math

>It's really, really funny how it makes me think of something completely abstract and unrelated (the isomorphism between l-2 spaces and the space of continuous square-integrable periodic functions)
I think it's hard to find two things in math which are entirely unrelated. That whole function space spiel just as much relates to character theory, Pontryagin duality, Rigged Hilbert spaces and eventually trickle into the position-momentum conundrum you have in quantum mechanics. What you look at then more concretely is this similar transform
https://en.wikipedia.org/wiki/Segal%E2%80%93Bargmann_space

>it starts by quantifying a simple continuous model (the continous vibrating string), and it makes a good deal of showcasing how you go from a continous model to infinitely countable quantas
You mean quantifying or quantizing here? The modes of a compact system are already countable discrete in the classical setting and you might also speak of "quantizing" here, so the language get's a bit fuzzy.
For telling things apart-sake, I'd speak of QM exactly at that point where it involves an algebra of observables (whatever the means of obtaining real measurement values is) that is a non-commutative algebra.

>>11448381
>but the textbook I'm reading
Which book?

I've recently ranted a bit about a history book here (and there's a follow-up video more concretely about the life of B. L. van der Waerden')
https://youtu.be/5zLr7hAnrZY