Non-Existence of Standard Wave Operators for Fractional Laplacian and Slowly Decaying Potentials

Non-Existence of Standard Wave Operators for Fractional Laplacian and Slowly Decaying Potentials

Year:    2019

East Asian Journal on Applied Mathematics, Vol. 9 (2019), Iss. 2 : pp. 233–240

Abstract

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/eajam.230418.170918

East Asian Journal on Applied Mathematics, Vol. 9 (2019), Iss. 2 : pp. 233–240

Published online:    2019-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    8

Keywords:    Scattering theory wave operator fractional Laplacian.