Scattering State Solutions of a Rationally Extended PT Symmetric Complex Potentials Using Potential Algebra Approach

Abstract

In this work, we extend the idea of the potential algebra approach (also known as group theoretic approach) to the exactly solvable rationally extended (RE) potentials and obtain their scattering state solutions. As an example we consider the RE Scarf-II potential, which is complex and PT symmetric and obtain its transmission and reflection amplitudes by considering the asymptotic behavior of the generators corresponding to the above algebra.