1

Any quantum state must be a square integrable function in order for it to be allowed. Is there any reason that this should be so? As far as I am aware, other $L^p$ spaces can have norms defined on them in a similar way to the norm of $L^2$. Is it just experimental fact that the probability of a position measurement, say, is given by$\int |\phi (x)| dx$, or is there some more foundational reason to restrict quantum states to $L^2$.

I apologize if I am unclear, I feel like I may be missing something fundamental here.

Qmechanic
  • 201,751
gabe
  • 1,232
  • Possible duplicates: http://physics.stackexchange.com/q/41719/2451 and links therein. – Qmechanic Feb 21 '17 at 18:50
  • To paraphrase: The problem is that we want to have a Hilbert space, and other $L^p$ spaces are note. Also, all separable Hilbert spaces are isomorphic to $L^2$, so since it's a convenient model, why not use this? – Martin Feb 21 '17 at 19:15
  • @Qmechanic somehow completely missed those when I searched. Thank you – gabe Feb 21 '17 at 20:58

0 Answers0