Abstract
We establish a physically meaningful representation of a quantum energy density for use in Quantum
Monte Carlo calculations. The energy density operator, de ned 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 di erences.
Using a model of delta-doped silicon (where dopant atoms form a thin plane) we show how interfacial
energies can be calculated more eciently 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.