Multiphase semiclassical approximation of an electron in a
one-dimensional crystalline lattice; I. Homogeneous problems;
vanishing exterior potentials.
Laurent Gosse and Peter A. Markowich
We present a computational approach for the WKB approximation of the
wave function of an electron moving in a periodic one-dimensional
crystal lattice. We derive a nonstrictly hyperbolic system for the
phase and the intensity where the flux functions originate from the
Bloch spectrum of the Schrödinger operator. Relying on the framework
of the multibranch entropy solutions introduced by Brenier and
Corrias, we compute efficiently multiphase solutions using well
adapted and simple numerical schemes. In this first part we present
computational results for vanishing exterior potentials which
demonstrate the effectiveness of the proposed method.
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- Laurent Gosse,
- Peter A. Markowich,
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- Submitted by:
April 7 2003.
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