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VLSI Design
Volume 9 (1999), Issue 4, Pages 427-434

Weak Limits of the Quantum Hydrodynamic Model

1Istituto di Analisi Numerica del C.N.R., Via Abbiategrasso 209, Pavia I-27100, Italy
2Johannes Kepler Universität Linz, Institut für Analysis und Numerik, Abtl. Differentialgleichungen, Altenberger Str. 69, Linz A-4040, Australia

Received 13 August 1997; Revised 1 December 1998

Copyright © 1999 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A numerical study of the dispersive limit of the quantum hydrodynamic equations for semiconductors is presented. The solution may develop high frequency oscillations when the scaled Planck constant is small. Numerical evidence is given of the fact that in such cases the solution does not converge to the solution of the formal limit equations.