High Quality Content by WIKIPEDIA articles! One would like to classify representations of the canonical commutation relation by two self-adjoint operators acting on separable Hilbert spaces, up to unitary equivalence. By Stone's theorem, there is a one-to-one correspondence between self-adjoint operators and (strongly continuous) one parameter unitary groups. Let Q and P be two self-adjoint operators satisfying the canonical commutation relation, and eit Q and eis P be the corresponding unitary groups given by functional calculus. A formal computation with power series shows that.

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