Commutator relations

alisa, you're supposed to show an attempted solution at the problem. That goes for your other threads as well.

What do you mean " if x=x". x=x by definition.

 

It's the coordinate representation in which the Hilbert space is [itex] L^{2}(\mathbb{R},dx) [/itex]. 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.

 

OK, so then it should read something like "If [itex]\hat{x}|\psi>=x|\psi>[/itex]...", right?

 

Exactly. That's the spectral equation, but nonetheless, yes.