  We establish a physically meaningful representation of a quantum energy
density for use in Quantum Monte Carlo calculations. The energy density
operator, defined in terms of Hamiltonian components and density operators,
returns the correct Hamiltonian when integrated over a volume containing a
cluster of particles. This property is demonstrated for a helium-neon "gas,"
showing that atomic energies obtained from the energy density correspond to
eigenvalues of isolated systems. The formation energies of defects or
interfaces are typically calculated as total energy differences. Using a model
of delta-doped silicon (where dopant atoms form a thin plane) we show how
interfacial energies can be calculated more efficiently with the energy
density, since the region of interest is small. We also demonstrate how the
energy density correctly transitions to the bulk limit away from the interface
where the correct energy is obtainable from a separate total energy
calculation.
