2013/09/26 by Rajesh Kumar Yadav, Avinash Khare, Bhabani Prasad Mandal · 1 citation
Physics and Astronomy · Mathematics · #hep-th #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1016/j.physleta.2014.11.009
published as Phys. Lett. A 379, 67 (2014) · 8 pages. Latex, No fig
arxiv created 2013/09/26 · arxiv updated 2015/09/30
We consider the rationally extended exactly solvable Eckart potentials which exhibit extended shape invariance property. These potentials are isospectral to the conventional Eckart potential. The scattering amplitude for these rationally ex- tended potentials is calculated analytically for the generalized mth (m = 1, 2, 3, ...) case by considering the asymptotic behavior of the scattering state wave functions which are written in terms of some new polynomials related to the Jacobi polyno- mials. As expected, in the m = 0 limit, this scattering amplitude goes over to the scattering amplitude for the conventional Eckart potential.