  We derive a lattice approximation for a class of equilibrium quantum
statistics describing the behaviour of any combination and number of bosonic
and fermionic particles with any sufficiently binding potential. We then
develop an intuitive Monte Carlo algorithm which can be used for the
computation of expectation values in canonical and Gaussian ensembles and give
lattice observables which will converge to the energy moments in the continuum
limit. The focus of the discussion is two-fold: in the rigorous treatment of
the continuum limit and in the physical meaning of the lattice approximation.
In particular, it is shown how the concepts and intuition of classical physics
can be applied in this sort of computation of quantum effects. We illustrate
the use of the Monte Carlo methods by computing canonical energy moments and
the Gaussian density of states for charged particles in a quadratic potential.
