The structure of the wave operator in four dimensions in the presence of resonances

We show that the wave operators for Schrödinger scattering in R 4 have a particular form which depends on the existence of resonances. As a consequence of this form, we determine the contribution of resonances to the index of the wave operator.

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Bibliographic Details
Published in:	Letters in mathematical physics Vol. 114; no. 5
Main Authors:	Alexander, Angus, Rennie, Adam
Format:	Journal Article
Language:	English
Published:	Dordrecht Springer Netherlands 19-10-2024 Springer Nature B.V
Subjects:	Complex Systems Geometry Group Theory and Generalizations Mathematical and Computational Physics Physics Physics and Astronomy Resonance scattering Theoretical Wave operator Resonances Schrödinger operators Fredholm index 81U05 35P25
Online Access:	Get full text
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Description
Summary:	We show that the wave operators for Schrödinger scattering in R 4 have a particular form which depends on the existence of resonances. As a consequence of this form, we determine the contribution of resonances to the index of the wave operator.
ISSN:	1573-0530 0377-9017 1573-0530
DOI:	10.1007/s11005-024-01868-y