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Classical lattice gas automata effectively simulate physical processes suchas diffusion and fluid flow (in certain parameter regimes) despite theirsimplicity at the microscale. Motivated by current interest in quantumcomputation we recently defined quantum lattice gas automata; in this paper weinitiate a project to analyze which physical processes these models caneffectively simulate. Studying the single particle sector of a one dimensionalquantum lattice gas we find discrete analogues of plane waves and wave packets,and then investigate their behaviour in the presence of inhomogeneouspotentials.Comment: 19 pages, plain TeX, 14 PostScript figures included with epsf.tex  (ignore the under/overfull \vbox error messages), two additional large  figures available upon reques

Quantum mechanics of lattice gas automata: One-particle plane waves and potentials