## 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

## 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.## References

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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: https://doi.org/10.1090/S0025-5718-1992-1122055-5
- MathSciNet review: 1122055