Long-range scattering matrix for Schrödinger-type operators

Nakamura, Shu

doi:10.2140/apde.2022.15.1725

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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

Vol. 15, No. 7, 2022