The quantum hydrodynamic smooth effective potential

An extension of the quantum hydrodynamic (QHD) model is discussed which is valid for classical potentials with discontinuities. The effective stress tensor for the QHD equations cancels the leading singularity in the classical potential at a barrier and leaves a residual smooth effective potential with a lower potential height in the barrier region. The smoothing makes the barrier partially transparent to the particle flow and provides the mechanism for particle tunneling in the QHD model.