Double Darboux method for the Taub continuum

TL;DR

This paper applies a novel double Darboux method to the quantum Taub model, creating a family of isospectral potentials with different scattering states, based on a modified Wheeler-DeWitt solution.

Contribution

It introduces a new application of the double Darboux method to generate isospectral potentials for the quantum Taub model, extending previous scattering solutions.

Findings

Generated a one-parameter family of isospectral Taub potentials

Modified existing Wheeler-DeWitt solutions for this context

Demonstrated different scattering states in the new potentials

Abstract

The strictly isospectral double Darboux method is applied to the quantum Taub model in order to generate a one-parameter family of strictly isospectral potentials for this case. The family we build is based on a scattering Wheeler-DeWitt solution first discussed by Ryan and collaborators that we slightly modified according to a suggestion due to Dunster. The strictly isospectral Taub potentials possess different (attenuated) scattering states with respect to the original Taub potential