Two-particle wave function as an integral operator and the random field approach to quantum correlations |
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Authors: | A. Yu. Khrennikov |
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Affiliation: | 1.International Center for Mathematical Modeling in Physics, Engineering, Economics, and Cognitive Science,Linnaeus University,V?xj?-Kalmar,Sweden |
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Abstract: | We propose a new interpretation of the wave function Ψ (x, y) of a two-particle quantum system, interpreting it not as an element of the functional space L 2 of square-integrable functions, i.e., as a vector, but as the kernel of an integral (Hilbert-Schmidt) operator. The first part of the paper is devoted to expressing quantum averages including the correlations in two-particle systems using the wave-function operator. This is a new mathematical representation in the framework of conventional quantum mechanics. But the new interpretation of the wave function not only generates a new mathematical formalism for quantum mechanics but also allows going beyond quantum mechanics, i.e., representing quantum correlations (including those in entangled systems) as correlations of (Gaussian) random fields. |
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