Existence, Uniqueness, and Semiclassical Limit for the Nonisentropic Steady‐State Quantum Hydrodynamic Model of Semiconductors

ABSTRACT In this paper, a quantum hydrodynamic system for particle density, current density, energy density, and electrostatic potential, coupled with a Poisson equation, is studied in spatial one‐dimensional real line. First, the existence and uniqueness of the stationary solution are proved in an appropriate Sobolev space. Then the semiclassical limit is investigated for the nonisentropic steady‐state quantum hydrodynamic system.