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Numerical analysis of the deterministic particle method applied to the Wigner equation


Authors: Anton Arnold and Francis Nier
Journal: Math. Comp. 58 (1992), 645-669
MSC: Primary 65M12; Secondary 35Q40, 81Q05
MathSciNet review: 1122055
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Abstract: The Wigner equation of quantum mechanics has the form of a kinetic equation with a pseudodifferential operator in a Fourier integral form which requires great care in the numerical approximation. This paper is concerned with the numerical analysis of the weighted particle method, introduced by S. Mas-Gallic and P. A. Raviart, applied to this equation. In particular, we will prove convergence of the method in a physically relevant case, where the Wigner equation models the quantum tunneling of electrons through a potential barrier.


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DOI: https://doi.org/10.1090/S0025-5718-1992-1122055-5
Article copyright: © Copyright 1992 American Mathematical Society