Revisiting generalized Hulthén potentials
Physique Nucléaire Théorique et Physique Mathématique, Université Libre de Bruxelles, Campus de la Plaine CP229, Boulevard du Triomphe, 1050, Brussels, Belgium
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Accepted: 17 January 2020
Published online: 7 February 2020
A relation between the deformed Hulthén potential and the Eckart one is used to write the bound-state wavefunctions of the former in terms of Jacobi polynomials and to calculate their normalization coefficients. The shape invariance property of the Eckart potential in standard first-order supersymmetric quantum mechanics allows to easily rederive the set of extended deformed Hulthén potentials, recently obtained by using the Darboux–Crum transformation, and to show that their spectra and normalized wavefunctions follow without any further calculation. The present approach considerably simplifies the previous derivation. Furthermore, by taking advantage of other known rational extensions of the Eckart potential obtained in first-order supersymmetric quantum mechanics, novel extensions of the deformed Hulthén potential are constructed, together with their bound-state spectra and wavefunctions. These new extensions belong to three different types, the first two being isospectral to some previously obtained extensions and the third one with an extra bound state below their spectrum.
© Società Italiana di Fisica (SIF) and Springer-Verlag GmbH Germany, part of Springer Nature, 2020