Is There an Infinity in Quantum Mechanics?

Is there an infinity in quanta mechanics? And i'm pretty sure the answer is yes, in terms of how physic think about it, but i'm not really sure how that fits in here. It seems like the universe that we inhabit is finite in a lot of ways, but we just don't know if there isn't an infinite set too. Sometimes mathematics can be used to make predictions into physical reality, but i don't necessarily think it has to. There's been a history of math coming up with kind of weird conjectures and and contexts that at first glance just make no sense.