  The correspondence between the integrability of classical mechanical systems
and their quantum counterparts is not a 1-1, although some close
correspondencies exist. If a classical mechanical system is integrable with
invariants that are polynomial in momenta one can construct a corresponding
commuting set of differential operators. Here we discuss some 2- or
3-dimensional purely quantum integrable systems (the 1-dimensional counterpart
is the Lame equation). That is, we have an integrable potential whose amplitude
is not free but rather proportional to $\hbar^2$, and in the classical limit
the potential vanishes. Furthermore it turns out that some of these systems
actually have N+1 commuting differential operators, connected by a nontrivial
algebraic relation. Some of them have been discussed recently by A.P. Veselov
et. al.} from the point of view of Baker-Akheizer functions.
