Improved analytical approximation to arbitrary l-state solutions of the Schrödinger equation for the hyperbolical potential

Abstract

A new approximation scheme to the centrifugal term is proposed to obtain the l = 0 bound-state solutions of the Schrödinger equation for an exponential-type potential in the framework of the hypergeometric method. The corresponding normalized wave functions are also found in terms of the Jacobi polynomials. To show the accuracy of the new proposed approximation scheme, we calculate the energy eigenvalues numerically for arbitrary quantum numbers n and l with two different values of the potential parameter σ0. Our numerical results are of high accuracy like the other numerical results obtained by using program based on a numerical integration procedure for short-range and long-range potentials. The energy bound-state solutions for the s-wave (l = 0) and σ0 = 1 cases are given.

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].…”

“…Obviously, the solutions in Refs. [44][45][46] are at best valid for R 0 = 0 in which the potential can be expanded in terms of hyperbolic functions [34,35,[44][45][46]. The standard WS potential turns to become the well-known Rosen-Morse potential shifted by the term −V 0 /2 (cf.…”

Arbitrary ℓ-state solutions of the Feynman propagator with the Deng-Fan molecular potential

“…To calculate the propagator K l given by equation (3) for = 0 states, we apply the following approximate scheme to the centrifugal term [4] :…”

“…However, when = 0 [1,2], the Schrödinger equation can only be solve approximately for different suitable approximation scheme [3,4]. This is due to the presence of the centrifugal term (1/r 2 ).…”

“…Motivated by the success in obtaining approximately the bound state solutions of the Feynman propagator with the Manning-Rosen and the Rosen-Morse potentials [5,6], we attempt here to solve the arbitrary -wave propagator with the Deng-Fan potential [7]. An improved approximation scheme for the centrifugal term is used as in [4] and non linear space-time transformations are applied.…”