Effective Quantum Observables

Details Effective Quantum Observables Effective Quantum Observables

1995-01-23

arxiv.org/abs/quant-ph/9501018v1

NuovoCim.B110:1397-1414,1995

Physics

Quantum Physics

TeX-file, 32 pages

Scientific paper

10.1007/BF02849839

Thought experiments about the physical nature of set theoretical counterexamples to the axiom of choice motivate the investigation of peculiar constructions, e.g. an infinite dimensional Hilbert space with a modular quantum logic. Applying a concept due to BENIOFF, we identify the intrinsically effective Hamiltonians with those observables of quantum theory which may coexist with a failure of the axiom of choice. Here a self adjoint operator is intrinsically effective, iff the Schroedinger equation of its generated semigroup is soluble by means of eigenfunction series expansions.

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