A one-dimensional lattice model for a quantum mechanical free particle
Abstract
Two types of particles, A and B with their corresponding antiparticles, are defined in a one dimensional 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 -->...B B B B B ... ; B --> A A A A A ... . 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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