Discrete wave mechanics: An introduction

Abstract

Discrete wave mechanics is formulated for particles in one-dimensional systems by use of a simple finite difference equation. The solutions involve wave vectors (instead of wave functions) as well as a newly defined “wave vector energy.” In the limit, as c → ∞, the treatment reduces to that of Schrödinger's wave mechanics. Specific calculations are made for completely free particles as well as for particles confined to a one-dimensional box. The results exhibit a striking compatibility with relativistic considerations. The wave vectors show properties that can be identified with particles and anti-particles—each possess identical probability distributions with energies that add up to zero.