On vibrational levels of the Deng-Fan molecular potential

Abstract In this study, we obtained the exact analytical eigenpairs of the Schrödinger equation with the Deng-Fan molecular potential in the absence of the centrifugal term ℓ ( ℓ + 1)/ r 2 . In the presence of the centrifugal term, the solutions cannot be expressed in terms of elementary or special functions. To approximate the eigenpairs for ℓ ≠ 0, researchers typically use an appropriate approximation scheme to deal with the centrifugal term. Nonetheless, the accuracy of the approximated eigenvalues is limited by the order of the approximation to the centrifugal term and is usually poor. Therefore, in this study, the centrifugal term is kept as it is and the Schrödinger equation is transformed into a form resembling the Laguerre differential equation. Thus, it is natural to approximate eigenpairs using the Laguerre basis in a pseudospectral picture. The numerical results reveal that the method can achieve accuracy to machine zero in either double- or quadruple-precision arithmetic.