The Stone–von Neumann Theorem

  • Brian C. Hall
Part of the Graduate Texts in Mathematics book series (GTM, volume 267)


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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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Brian C. Hall
    • 1
  1. 1.Department of MathematicsUniversity of Notre DameNotre DameUSA

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