Abstract
We consider a quantum system described by the relativistic Schrödinger operator and interaction potential. When a slowly decaying potential function is given, we prove the nonexistence of the wave operators, under the assumption that the Dollard-type modified wave operators exist and that they are asymptotically complete. This nonexistence indicates the threshold between the short-range and long-range behavior.
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Acknowledgements
This work was partially supported by the Grant-in-Aid for Young Scientists (B) #16K17633 from JSPS. The author would like to thank the referees for the valuable comments and suggestions.
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Ishida, A. (2020). Nonexistence Result for Wave Operators in Massive Relativistic System. In: Miranda, P., Popoff, N., Raikov, G. (eds) Spectral Theory and Mathematical Physics. Latin American Mathematics Series(). Springer, Cham. https://doi.org/10.1007/978-3-030-55556-6_9
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DOI: https://doi.org/10.1007/978-3-030-55556-6_9
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