Schrodinger operators and associated hyperbolic pencils

TL;DR

This paper introduces hyperbolic quadratic pencils for a broad class of Schrödinger operators by making the coupling constant energy-dependent, simplifying scattering theory problems and providing applications to the original operators.

Contribution

It presents a novel approach of energy-dependent coupling in Schrödinger operators via hyperbolic quadratic pencils, easing the analysis of scattering problems.

Findings

Simplified scattering theory for Schrödinger operators using hyperbolic pencils

Established applications of these pencils to original Schrödinger operators

Provided new methods for analyzing spectral properties

Abstract

For a large class of Schrodinger operators, we introduce the hyperbolic quadratic pencils by making the coupling constant dependent on the energy in the very special way. For these pencils, many problems of scattering theory are easier to study. Then, we give some applications to the original Schrodinger operators.