A Hilbert Space Realization of Nonlinear Quantum Mechanics as Classical Extension of Its Linear Counterpart

Author: Del Seta M.   Cattaneo G.  

Publisher: Springer Publishing Company

ISSN: 0020-7748

Source: International Journal of Theoretical Physics, Vol.39, Iss.3, 2000-03, pp. : 621-640

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Abstract

This paper studies the state-effect-probability structure associated with the quantum mechanics of nonlinear (homogeneous, in general nonadditive) operators on a Hilbert space. Its aim is twofold: to provide a concrete representation of the features of nonlinear quantum mechanics on a Hilbert space, and to show that the properties of the nonlinear version of quantum mechanics here described have the structure of a classical logic.