Long-range scattering for discrete Schr\"odinger operators

TL;DR

This paper develops a long-range scattering theory for discrete Schrödinger operators on the lattice, introducing time-independent modifiers to establish the existence and completeness of modified wave operators.

Contribution

It introduces a novel approach using time-independent modifiers to construct a comprehensive long-range scattering theory for discrete Schrödinger operators.

Findings

Existence of modified wave operators proven

Completeness of the wave operators established

Framework applicable to Schrödinger operators on Z^N"

Abstract

In this paper, we define time-independent modifiers to construct a long-range scattering theory for discrete schr\"odinger operators on the square lattice $\mathbb{Z}^N$. We prove the existence and completeness of modified wave operators in terms of the above mentioned time-independent modifiers.