Scattering theory for the Wigner equation | Zendy

Emamirad Hassan | Zendy; Rogeon Philippe | Zendy

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Scattering theory for the Wigner equation

Author(s) -

Emamirad Hassan,

Rogeon Philippe

Publication year - 2005

Publication title -

mathematical methods in the applied sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.719

H-Index - 65

eISSN - 1099-1476

pISSN - 0170-4214

DOI - 10.1002/mma.601

Subject(s) - formalism (music) , mathematics , mathematical physics , wigner distribution function , completeness (order theory) , scattering , wave equation , scattering theory , mathematical analysis , pure mathematics , quantum mechanics , physics , quantum , art , musical , visual arts

We prove that the Wigner equation is well‐posed in L p (ℝ 2 n ) for some potential V . From the formalism established by Markovich, we show the completeness of wave operators for the Wigner equation in L 2 . Using estimations proved by Castella and Perthame, on the one hand, and the L p → L q estimations for the Schrödinger group, on the other hand, we prove the existence of the wave operators in L 2, p spaces. Copyright © 2005 John Wiley & Sons, Ltd.

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