Eigenphase preserving two-channel SUSY transformations

TL;DR

This paper introduces a novel supersymmetric transformation for two-channel scattering problems that preserves eigenphase shifts while modifying the mixing parameter, offering new tools for quantum scattering analysis.

Contribution

It presents a new eigenphase preserving SUSY transformation that alters the mixing parameter without changing eigenphase shifts in two-channel scattering.

Findings

The transformation preserves eigenphase shifts.

It modifies the mixing parameter.

Applicable to equal-threshold two-channel scattering.

Abstract

We propose a new kind of supersymmetric (SUSY) transformation in the case of the two-channel scattering problem with equal thresholds, for partial waves of the same parity. This two-fold transformation is based on two imaginary factorization energies with opposite signs and with mutually conjugated factorization solutions. We call it an eigenphase preserving SUSY transformation as it relates two Hamiltonians, the scattering matrices of which have identical eigenphase shifts. In contrast to known phase-equivalent transformations, the mixing parameter is modified by the eigenphase preserving transformation.