Dynamic representation of the Weyl solution for the Schr\"odinger operator on the semi-axis

TL;DR

This paper presents a new representation formula for the Weyl solution of the Schrödinger operator on the semi-axis, linking it to wave equation initial-boundary value problems for specific potentials.

Contribution

It introduces a novel approach connecting Weyl solutions to wave equation problems, providing a new analytical tool for Schrödinger operators with certain potentials.

Findings

Derived a representation formula for the Weyl solution.

Established relations between Schrödinger and wave equations.

Applicable to specific classes of potentials.

Abstract

We derive a representation formula for the Weyl solution to the Schr\"odinger operator on the semi-axis for certain classes of potentials. Our approach is based on relations with the initial-boundary value problem for the wave equation with the same potential on the half-line.