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.
doubled” the total Hilbert space: in the first case by extending the semi-infinite real axis to the whole real axis, in the second case by using an extra (“ancilla
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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.