# Resonances for the one dimensional Schr\"odinger operator with the matrix-valued complex square-well potential

## TL;DR

This paper investigates the distribution and properties of resonances in non-selfadjoint Schr"odinger operators with matrix-valued square-well potentials, providing explicit formulas and asymptotic laws.

## Contribution

It explicitly computes the Jost function, derives equations for resonances, and establishes a Weyl Law for their distribution in the complex plane.

## Key findings

- Explicit formulas for the Jost function
- Complex transcendental equations for resonances
- Weyl Law for resonance counting

## Abstract

We study the resonances of (generally, non-selfadjoint) Schr\"odinger operators with matrix-valued square-well potentials. We compute explicitly the Jost function and derive complex transcendental equations for the resonances. We prove several results concerning the distribution of resonances in the complex plane. We compute the multiplicity of resonances and prove a version of the Weyl Law for the number of resonances.