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The Wave Function as Matter Density: Ontological Assumptions and Experimental Consequences

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Abstract

The wavefunction is the central mathematical entity of quantum mechanics, but it still lacks a universally accepted interpretation. Much effort is spent on attempts to probe its fundamental nature. Here I investigate the consequences of a matter ontology applied to spherical masses of constant bulk density. The governing equation for the center-of-mass wavefunction is derived and solved numerically. The ground state wavefunctions and resulting matter densities are investigated. A lowering of the density from its bulk value is found for low masses due to increased spatial spreading. A discussion of the possibility to experimentally observe these effects is given and the possible consequences for choosing an ontological interpretation for quantum mechanics are commented upon.

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Notes

  1. A different treatment of the integral kernel was recently proposed in [54] where the expressions 20 were rederived.

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  1. Dalarna University, 79188, Falun, Sweden

    Markku Jääskeläinen

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Jääskeläinen, M. The Wave Function as Matter Density: Ontological Assumptions and Experimental Consequences. Found Phys 45, 591–610 (2015). https://doi.org/10.1007/s10701-015-9884-7

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