Lattice Simulations of the Quantum Microcanonical Ensemble

We propose a method for the numerical computation of microcanonical expectation values--i.e. averages over energy eigenstates with the same eigenvalue-without any prior knowledge about the spectrum of the Hamiltonian. This is accomplished by first defining a new Gaussian ensemble to approximate the microcanonical one. We then develop a ``lattice theory'' for this Gaussian ensemble and propose a Monte Carlo integration of the expectation values of the lattice theory.