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Long-range scattering matrix for Schrödinger-type operators

Shu Nakamura
Vol. 15 (2022), No. 7, 1725–1762
DOI: 10.2140/apde.2022.15.1725
Abstract

We show that the scattering matrix for a class of Schrödinger-type operators with long-range perturbations is a Fourier integral operator with phase function which is the generating function of the modified classical scattering map.

Keywords
scattering matrix, long-range scattering, Fourier integral operators
Mathematical Subject Classification 2010
Primary: 35P25
Secondary: 58J50, 81U05
Milestones
Received: 18 March 2020
Revised: 4 February 2021
Accepted: 25 March 2021
Published: 5 December 2022
Authors
Shu Nakamura
Department of Mathematics
Gakushuin University
Tokyo
Japan