Abstract
The Stone–von Neumann theorem is a uniqueness theorem for operators satisfying the canonical commutation relations. Suppose A and B are two self-adjoint operators on H satisfying \([A,B] = i\hslash I.\) Suppose also that A and B act irreducibly on H,meaning that the only closed subspaces of H invariant under A and B are {0} and H.Then provided that certain technical assumptions hold (the exponentiated commutation relations)
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Hall, B.C. (2013). The Stone–von Neumann Theorem. In: Quantum Theory for Mathematicians. Graduate Texts in Mathematics, vol 267. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7116-5_14
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DOI: https://doi.org/10.1007/978-1-4614-7116-5_14
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