Abstract
In a previous publication (Boletin de la Sociedad Matematica Mexicana 1975) it was established that any weakly stationary linearly regular stochastic process is unitarily equivalent to a quantum mechanical momentum evolution. The object of the present note is, as promised in the previous publication, to amplify some of the details concerning the just mentioned interesting connection, giving in particular a direct proof of the Szego-Kolmolgorov-Krein characterization of regular stationary processes. We also show that although the so-called decaying states without regeneration do not exist for unstable quantum systems, they are natural for regular stationary processes.
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Gustafson, K., Misra, B. Canonical commutation relations of quantum mechanics and stochastic regularity. Lett Math Phys 1, 275–280 (1976). https://doi.org/10.1007/BF00398481
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DOI: https://doi.org/10.1007/BF00398481