Quantum hydrodynamic extensions of classical electrogasdynamics to include quantum mechanical effects like tunneling through potential barriers and charge buildup in quantum wells will be presented. The quantum hydrodynamic models are derived by a moment expansion of the Wigner-Boltzmann transport equation, based on a thermal equilibrium "quantum Maxwellian," and involve dispersive Schrodinger-mode terms and/or a hyperbolic-mode smoothing of the classical potential energy, as well as a parabolic heat conduction term. The competing effects of dispersion vs. diffusion vs. hyperbolicity will be emphasized.

Simulations of the resonant tunneling diode using these models will be presented, which demonstrate the signature of quantum resonance and tunneling. This work is joint with Christian Ringhofer.

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