Two state scattering problem to Multi-channel scattering problem: Analytically solvable model

TL;DR

This paper introduces a general analytical method for solving multi-channel scattering problems, extending from simple two-state cases to more complex multi-channel scenarios, using delta function coupling.

Contribution

It presents a novel, exact analytical approach for multi-channel scattering problems, expanding the scope from two-state to general multi-channel systems.

Findings

Derived an exact analytical solution for two-state scattering with delta coupling.

Extended the model to general one-dimensional multi-channel scattering.

Provided a framework applicable to complex scattering scenarios.

Abstract

Starting from few simple examples we have proposed a general method for finding an exact analytical solution for the two state scattering problem in presence of a delta function coupling. We have also extended our model to deal with general one dimensional multi-channel scattering problems.