Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



The Schrödinger with variable mass model: mathematical analysis and semi-classical limit

Author: Jihène Kefi
Journal: Quart. Appl. Math. 62 (2004), 201-220
MSC: Primary 82C70; Secondary 34B15
DOI: https://doi.org/10.1090/qam/2054596
MathSciNet review: MR2054596
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Abstract: In this paper, we propose and analyze a one-dimensional stationary quantum-transport model: the Schrödinger with variable mass. In the first part, we prove the existence of a solution for this model, with a self-consistent potential determined by the Poisson problem, whereas, in the second part, we rigorously study its semi-classical limit which gives us the kinetic model limit. The rigorous limit was based on the analysis of the support of the Wigner transform.

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DOI: https://doi.org/10.1090/qam/2054596
Article copyright: © Copyright 2004 American Mathematical Society

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