  We investigate (2+1)-d Hamiltonian lattice gauge theory using a class of
Hamiltonians having exactly known vacuum states. These theories are shown to
have a wide range of possible classical continuum limits which differ from that
of the standard Kogut-Susskind Hamiltonian. This conclusion is at variance with
some previously published results. We examine the quantum continuum behavior of
these theories by both analytic and numerical methods including plaquette space
integration and standard Monte Carlo techniques. String tension and variational
estimates for the $J^{\rm PC}=0^{++}$ glueball spectra are presented for SU(3).
We find that in spite of the wide range of classical behavior predicted, these
theories correspond to only two distinct quantum systems in the weak coupling
limit. One of these quantum limits gives string tensions and glueball states
which show scaling in weak coupling which agrees with the perturbative
prediction for the (2+1)-d problem.
