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 -
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.