Scattering theory for Schr\"odinger operators on steplike, almost periodic infinite-gap backgrounds

TL;DR

This paper develops a scattering theory for 1D Schrödinger operators with steplike, almost periodic infinite-gap potentials, advancing understanding of wave behavior in complex, non-uniform quantum systems.

Contribution

It introduces a new scattering framework for Schrödinger operators with steplike, almost periodic infinite-gap backgrounds, extending previous models to more complex potentials.

Findings

Established a direct scattering theory for steplike, almost periodic potentials.

Analyzed asymptotic behaviors of solutions on different half-axes.

Provided mathematical tools for studying wave propagation in complex media.

Abstract

We develop direct scattering theory for one-dimensional Schr\"odinger operators with steplike potentials, which are asymptotically close to different Bohr almost periodic infinite-gap potentials on different half-axes.