Green's functions for reflectionless potentials and addition of boundstates to powerlaw potentials to find Supersymmetric partners

TL;DR

This paper constructs and analyzes Green's functions for reflectionless and power law potentials, explores their supersymmetric partners, and introduces methods to add bound states at zero energy, advancing the understanding of quantum potential relationships.

Contribution

It introduces a novel approach to constructing SUSY partner potentials with added bound states at zero energy for power law potentials.

Findings

Green's functions for reflectionless potentials are explicitly constructed.

SUSY partner potentials with an additional zero-energy bound state are developed.

Sum rules for eigenvalues in these potentials are derived.

Abstract

Green's functions for reflectionless potentials are constructed and analyzed. Green's functions for power law potentials, their Super Symmetric partners and sum rules for eigenvalues are examined. The SUSY partner potentials to power law potentials which have an additional bound state at $E=0$ are constructed.