Ro-vibrational energy analysis of Manning–Rosen and Pöschl–Teller potentials with a new improved approximation in the centrifugal term

Analytical solution of $D$ dimensional Schrödinger equation for Eckart potential with a new improved approximation in centrifugal term

“…By construction, f 4 approximation is more effective around r = r 0 region [5,29,35,36]. In this article, we propose a new approximation to the centrifugal term, following our previous works [23,24],…”

“…( 7), we will use a transformation, s = e −r/a , and a set of functions, 1, s 1−s , s 2 (1−s) 2 , for which the centrifugal term is approximated in different forms, such as Greene-Aldrich [28], Pekeris-type [29]. Recently, the authors have proposed an intuitive combination of these two approximations [23,24] with considerable success.…”

“…Likewise, from panels (I), (J), it is inferred that f 4 , f (b) 5 are superior in the neighborhood of r = r 0 . Thus f 5 remains quite accurate over the entire effective domain of r [23,24], which has been defined in our previous communications [37,38]. Throughout the article, for sake of convenience, f 5 approximations will be used for various sets of {λ 1 , λ 2 , λ 3 , λ 4 }.…”

“…At first, we would like to make an analysis and test performance of a recently developed, simple approximation for centrifugal term in the context of Eckart potential. So far, this has been applied to shifted Deng-Fan, Manning-Rosen and Pöschl-Teller molecular potentials [23,24]. This will extend the scope of applicability to a wider range of physical systems.…”

“…The article is organized as follows: Sec. II gives an overview of various approximations to the centrifugal term, including the newly proposed one [23,24], for solving the SE for Eckart potential, within the NU method. The resultant analytic expressions are derived for radial wave functions, eigenvalues, normalization constants.…”