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Volume 9, Issue 2
Non-Existence of Standard Wave Operators for Fractional Laplacian and Slowly Decaying Potentials

Atsuhide Ishida

DOI: 10.4208/eajam.230418.170918

East Asian J. Appl. Math., 9 (2019), pp. 233-240.

Published online: 2019-03

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  • 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.

  • Keywords

Scattering theory, wave operator, fractional Laplacian.

  • AMS Subject Headings

81Q10, 81U05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-9-233, author = {Atsuhide Ishida}, title = {Non-Existence of Standard Wave Operators for Fractional Laplacian and Slowly Decaying Potentials}, journal = {East Asian Journal on Applied Mathematics}, year = {2019}, volume = {9}, number = {2}, pages = {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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.230418.170918 }, url = {http://global-sci.org/intro/article_detail/eajam/13079.html} }
TY - JOUR T1 - Non-Existence of Standard Wave Operators for Fractional Laplacian and Slowly Decaying Potentials AU - Atsuhide Ishida 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.

Atsuhide Ishida. (2019). Non-Existence of Standard Wave Operators for Fractional Laplacian and Slowly Decaying Potentials. East Asian Journal on Applied Mathematics. 9 (2). 233-240. doi:10.4208/eajam.230418.170918
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