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- Thread starter alisa
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quantumdude

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given that [x,p]=ih, show that if x=x,

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

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What do you mean " if x=x". x=xby 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.

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quantumdude

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

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

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