Discrete wave mechanics: An introduction.
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 --> infinity, 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.
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Department of Chemistry, B-017, University of California at San Diego, La Jolla, CA 92093.