Abstract
We introduce and solve a lattice version of an easily soluble one-dimensional continuum quantum system with a periodic potential. The relationship of the one problem to the other is identical to the relationship of the one-dimensional quantum many-body lattice gas recently introduced by Shastry (Phys. Rev. Lett. 60, 639 (1988)) and by Haldane (Phys. Rev. Lett. 60, 635 (1988)) to the one-dimensional quantum many-body continuum gas earlier solved by Sutherland. Thus it is hoped that by understanding the ''missing'' states in this simple case, we might better understand the missing states in the more complicated many-body case, which in many instances comprise all the states. The results are not encouraging.
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