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We derive a lattice approximation for a class of equilibrium quantumstatistics describing the behaviour of any combination and number of bosonicand fermionic particles with any sufficiently binding potential. We thendevelop an intuitive Monte Carlo algorithm which can be used for thecomputation of expectation values in canonical and Gaussian ensembles and givelattice observables which will converge to the energy moments in the continuumlimit. The focus of the discussion is two-fold: in the rigorous treatment ofthe continuum limit and in the physical meaning of the lattice approximation.In particular, it is shown how the concepts and intuition of classical physicscan be applied in this sort of computation of quantum effects. We illustratethe use of the Monte Carlo methods by computing canonical energy moments andthe Gaussian density of states for charged particles in a quadratic potential.Comment: 23 pages, 1 figure, uses iopart.cls and epsf.st

Lattice computation of energy moments in canonical and Gaussian quantum statistics