Approximate l-state solutions of the D-dimensional Schrödinger equation for Manning-Rosen potential

Abstract

The Schrödinger equation in D-dimensions for the Manning-Rosen potential with the centrifugal term is solved approximately to obtain bound states eigensolutions (eigenvalues and eigenfunctions). The Nikiforov-Uvarov (NU) method is used in the calculations. We present numerical calculations of energy eigenvalues to two-and four-dimensional systems for arbitrary quantum numbers n and l with three different values of the potential parameter α. It is shown that because of the interdimensional degeneracy of eigenvalues, we can also reproduce eigenvalues of a upper/lower dimensional system from the well-known eigenvalues of a lower/upper dimensional system by means of the transformation (n, l, D) → (n, l ± 1, D ∓ 2). This solution reduces to the Hulthén potential case.

The relativistic bound and scattering states of the Manning-Rosen potential with an improved new approximate scheme to the centrifugal term

“…Soylu et al [21] have obtained the analytical solutions of the Klein-Gordon equation for the equal scalar and vector Rosen-Morse potential and Eckart potential as well as parity-time symmetric version of these potentials by using the asymptotic iteration method. As mentioned above, the Manning-Rosen potential cannot be solved exactly for the arbitrary states except for an approximation to the centrifugal term [7,11,20]. However, It should be noted that the results obtained previously [7,11] are in good agreement with those obtained by using the program based on a numerical integration procedure [22] for the short-range potential, but the difference between them appears for the long-range potential.…”

“…The −wave bound and scattering states of the Schrödinger equation for this potential have been carried out by using the factorization method [17], the function analysis method [18] and path integral approach [19], respectively. In addition, Ikhdair and Sever have also studied the arbitrary −wave solutions of the D-dimensional Schrödinger equation with the Manning-Rosen potential [20] by Nikiforov-Uvarov approach. Soylu et al [21] have obtained the analytical solutions of the Klein-Gordon equation for the equal scalar and vector Rosen-Morse potential and Eckart potential as well as parity-time symmetric version of these potentials by using the asymptotic iteration method.…”

Approximate analytical solutions of the generalized Woods-Saxon potentials including the spin-orbit coupling term and spin symmetry

“…The NU method has been used to solve the Schrödinger [34,35], KG [36][37][38][39][40]61] and Dirac 1 [55] wave equations for central and non-central potentials. Let us briefly outline the basic concepts of the method [62].…”

Any ℓ-state solutions of the Eckart potential via asymptotic iteration method

“…Some of these potentials are the Eckart potential [1][2][3][4], Manning-Rosen potential [5][6][7], Morse potential [8,9] etc. Several methods, such as the Nikiforov-Uvarov method, asymptotic iteration method, supersymmetry, etc, have been used to solve the differential equations arising from these consideration.…”