Premium
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.