TY - JOUR
T1 - Non-Existence of Standard Wave Operators for Fractional Laplacian and Slowly Decaying Potentials
JO - East Asian Journal on Applied Mathematics
VL - 2
SP - 233
EP - 240
PY - 2019
DA - 2019/03
SN - 9
DO - http://doi.org/10.4208/eajam.230418.170918 
UR - https://global-sci.org/intro/article_detail/eajam/13079.html
KW - Scattering theory, wave operator, fractional Laplacian.
AB - <p style="text-align: justify;">Quantum systems described by the fractional powers of the negative Laplacian and the interaction potentials are considered. If the potential function slowly decays
and the Dollard-type modified wave operators exist and are asymptotically complete, we
prove that the factional Laplacian does not possess the standard wave operators. This
result suggests the borderline between the short- and long-range behaviour.</p>