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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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.