The European Physical Journal D (EPJ D)

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Eur. Phys. J. D 8, 165-168

A one-dimensional lattice model for a quantum mechanical free particle

A.C. de la Torre - A. Daleo

Departamento de Física, Universidad Nacional de Mar del Plata, Funes 3350, 7600 Mar del Plata, Argentina
dltorre@mdp.edu.ar

Received 25 March 1999 and Received in final form 20 August 1999

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: $A \rightarrow \cdots \bar{B} B \bar{B} B \bar{B} \cdots$ ; $B \rightarrow \cdots A \bar{A} A \bar{A} A \cdots$ . It is shown that the combined distribution of these particles obeys the time evolution of a free particle as given by quantum mechanics.

PACS
03.65.Bz Foundations, theory of measurement, miscellaneous theories (including Aharonov-Bohm effect, Bell inequalities, Berry's phase) - 03.65.Ca Formalism