  We derive the phase space particle density operator in the 'droplet' picture
of bosonization in terms of the boundary operator. We demonstrate that it
satisfies the correct algebra and acts on the proper Hilbert space describing
the underlying fermion system, and therefore it can be used to bosonize any
hamiltonian or related operator. As a demonstration we show that it reproduces
the correct excitation energies for a system of free fermions with arbitrary
dispersion relations.
