Exact normalized eigenfunctions for general deformed Hulthén potentials

Abstract

The exact solutions of Schrödinger's equation with the deformed Hulthén potential $V_q(x)=-\mu e^{-\delta x}/(1-q{e}^{-\delta x}),\delta ,\mu ,q>0$ are given, along with a closed--form formula for the normalization constants of the eigenfunctions for arbitrary $q>0$. The Crum-Darboux transformation is then used to derive the corresponding exact solutions for the extended Hulthén potentials $V(x)=-\mu e^{-\delta x}/(1-q{e}^{-\delta x})+qj(j+1)e^{-\delta x}/(1-q{e}^{-\delta x}{)}^2,j=0,1,2,\dots .$ A general formula for the new normalization condition is also provided.

14 pages, two figures