All separable Hilbert spaces of given dimension being isomorphic implies exactly six basic generalized coordinate operators and seven coordinate-momentum pairs via self-adjoint or Neumark extensions.
That this is so, follows, in physicists’ notation, from ⟨p′|p⟩ = δ(p′ − p)
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All Hilbert spaces are the same: consequences for generalized coordinates and momenta
All separable Hilbert spaces of given dimension being isomorphic implies exactly six basic generalized coordinate operators and seven coordinate-momentum pairs via self-adjoint or Neumark extensions.