From a 1D Completed Scattering and Double Slit Diffraction to the Quantum-Classical Problem for Isolated Systems

Foundations of Physics 41 (9):1502-1520 (2011)

Abstract
By probability theory the probability space to underlie the set of statistical data described by the squared modulus of a coherent superposition of microscopically distinct (sub)states (CSMDS) is non-Kolmogorovian and, thus, such data are mutually incompatible. For us this fact means that the squared modulus of a CSMDS cannot be unambiguously interpreted as the probability density and quantum mechanics itself, with its current approach to CSMDSs, does not allow a correct statistical interpretation. By the example of a 1D completed scattering and double slit diffraction we develop a new quantum-mechanical approach to CSMDSs, which requires the decomposition of the non-Kolmogorovian probability space associated with the squared modulus of a CSMDS into the sum of Kolmogorovian ones. We adapt to CSMDSs the presented by Khrennikov (Found. Phys. 35(10):1655, 2005) concept of real contexts (complexes of physical conditions) to determine uniquely the properties of quantum ensembles. Namely we treat the context to create a time-dependent CSMDS as a complex one consisting of elementary (sub)contexts to create alternative subprocesses. For example, in the two-slit experiment each slit generates its own elementary context and corresponding subprocess. We show that quantum mechanics, with a new approach to CSMDSs, allows a correct statistical interpretation and becomes compatible with classical physics
Keywords Tunneling  Hartman paradox  Wave-particle duality  Two-slit experiment  Quantum ensembles  Complex and elementary contexts  Kolmogorovness  Coherent superpositions of microscopically distinct states
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DOI 10.1007/s10701-011-9564-1
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Zitterbewegung in Quantum Mechanics.David Hestenes - 2010 - Foundations of Physics 40 (1):1-54.

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