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