  We consider M systems (each an electron in a long square cylinder) uniformly
arranged on a ring and with Coulomb interactions. Exact straightforward
numerical time-dependent perturbation calculation of a single N-level
($\lesssim 7$) system, with no (random) phase assumptions, system show a
Boltzman distribution. We exploit the physical ring symmetry and develop
several hierarchical physical equation set so of increasing generality and
(computation) speed. Given the impressive history of theoretical
quantum-mehanical statistical mechanics, our results might seem surprising, but
we observe that accurate calculation of correct physical equations should mimic
Nature.
