A one-dimensional lattice model for a quantum mechanical free particle
Departamento de Física, Universidad Nacional de Mar del Plata,
Funes 3350, 7600 Mar del Plata, Argentina
Revised: 20 August 1999
Published online: 13 August 2013
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: ; . 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
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000