Numerical analysis of the deterministic particle method applied to the Wigner equation. (English) Zbl 0763.65092
The paper deals with the numerical analysis of the weighted particle method, applied to the Wigner equation. A priori estimates of the exact solution in \(W^{m,p}\) spaces are presented. A convergence analysis of the particle method for a smooth potential is also provided. The paper ends with a convergence proof of the one-dimensional particle method for a rectangular potential barrier where the potential is not smooth: \(V(x)=1\) if \(x\in(-{1\over 2},{1\over 2})\) and \(=0\) else.
Reviewer: L.Vazquez (Madrid)
MSC:
| 65Z05 | Applications to the sciences |
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
| 35S05 | Pseudodifferential operators as generalizations of partial differential operators |
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
| 35Q40 | PDEs in connection with quantum mechanics |
| 81S30 | Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics |
Keywords:
transport phenomena; pseudodifferential operator; quantum tunneling of electrons; potential barrier; weighted particle method; Wigner equation; convergenceReferences:
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