The “smooth” quantum hydrodynamic (QHD) model is an extension of the classical hydrodynamic model for semiconductor devices which can handle in a mathematically rigorous way the discontinuities in the classical potential energy which occur at heterojunction barriers in quantum semiconductor devices. Smooth QHD model simulations of the resonant tunneling diode exhibit negative differential resistance—the experimental signal for quantum resonance effects. Resonant tunneling is analyzed in fluid dynamical terms from the point of view of the smooth QHD transport equations.