Abstract
Two types of particles, A and B with their corresponding antiparticles, are defined in a onedimensional cyclic lattice with an odd number of sites. In each step of time evolution, each particle acts as a source for the polarization field of the other type of particle with nonlocal action but with an effect decreasing with the distance: \(A \to \cdots \bar BB\bar BB\bar B \cdots ;B \to \cdots A\bar AA\bar AA \cdots \). It is shown that the combined distribution of these particles obeys the time evolution of a free particle as given by quantum mechanics.
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de la Torre, A.C., Daleo, A. A one-dimensional lattice model for a quantum mechanical free particle. Eur. Phys. J. D 8, 165–168 (2000). https://doi.org/10.1007/s10053-000-8805-1
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DOI: https://doi.org/10.1007/s10053-000-8805-1