Commutator relations

given that [x,p]=ih, show that if x=x, p has the representation p=-iħ∂/∂x+f(x) where f(x) is an arbitrary function of x

Tom Mattson
Staff Emeritus
Gold Member
alisa, you're supposed to show an attempted solution at the problem. That goes for your other threads as well.

given that [x,p]=ih, show that if x=x,
What do you mean " if x=x". x=x by definition.

dextercioby
Homework Helper
What do you mean " if x=x". x=x by definition.
It's the coordinate representation in which the Hilbert space is $L^{2}(\mathbb{R},dx)$. The "x" operator is realized by a multiplication by "x". She's asked to prove that the most general representation of the momentum operator in this Hilbert space is the one written there.

Tom Mattson
Staff Emeritus
OK, so then it should read something like "If $\hat{x}|\psi>=x|\psi>$...", right?