Does QM Use n-Dimensional or Infinite Dimensional Integrals?

[benorin]

Much as the title of this thread asks: does quantum mechanics use n-dimensional or infinite dimensional integrals? I'm merely curious as I studied the n-dimensional case as a hobby and wondered if I'd ever get to use it for anything cool like QM. If so, please maybe post one such integral so I can play with it. Thanks.

 

[A. Neumaier]

It uses both. The Feynman path integral is always infinite-dimensional, but the integrals defining inner products are (for systems with finitely many particles only) always finite-dimensional.