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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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The 2020 MCQ for Mathematics of Computation is 1.98.

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Numerical analysis of the deterministic particle method applied to the Wigner equation
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by Anton Arnold and Francis Nier PDF
Math. Comp. 58 (1992), 645-669 Request permission


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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Additional Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Math. Comp. 58 (1992), 645-669
  • MSC: Primary 65M12; Secondary 35Q40, 81Q05
  • DOI:
  • MathSciNet review: 1122055