Approximate Solution of the Schrödinger Equation with Rosen-Morse Potential Including the Centrifugal Term

Abstract

We derive approximate analytical solutions of the Schrödinger equation with Rosen-Morse potential via the Nikiforov-Uvarov method. The bound state energy eigenvalues are given in a closed form and the corresponding eigenfunctions are obtained in terms of the generalize Jacobi Polynomials and hypergeometrical function.

Approximate Solution of Schrodinger Equation for Hulthen Potential plus Eckart Potential with Centrifugal Term in terms of Finite Romanovski Polynomials

“…By setting the coefficient of in equation (18) then equation (17) reduces to the Romanovski equation expressed in equation (10). By comparing the parameters between equations (10) and (17) we obtain the following relation: …”

Analytical solution of energy eigen value, eigen function and angular wave function of Dirac equation with Rosen Morse plus Rosen Morse potential in terms of Romanovski polynomials for exact spin symmetry

“…Romanovski polynomials were discovered in 1884 by Routh in the form of complexified Jacobi polynomials on the unit circle in the complex plane and were then rediscovered as real polynomials by Romanovski in a statistics framework (Ikot & Akpabio (2010). The Romanovski polynomials are built from The generalized hypergeometric equation is given,…”

“…The potentials that can be used sucs as hyperbolic Scarf Potential, Manning Rosen, Rosen Morse, etc. The bound state energy spectra of these potentials have been investigated by Supersymetri method (Cari, Suparmi & H. Marini, 2012), Nikivorof-Uvarof (Ikot & Akpabio, 2010), Laplace Transformation Method (Eshghi, Hamzavi & Ikhdair, 2012). Romanovsky polynomials (David, 2009), WKB Method (Sadeghi, Pahlavani, Naderi, et al, 2005).…”

Solutions of Schrödinger Equation with Generalized Inverted Hyperbolic Potential

“…Among such potentials are Poschl-Teller, Rosen-Morse and Scarf potential, which have been studied extensively in the literatures, [5][6][7][8][22][23][24][25]. However, some of these hyperbolic potentials are exactly solvable or quasi-exactly solvable and their bound state solutions have been reported, [3,4,11,13,[26][27][28]. We seek to present and study a generalized hyperbolic potential which other potentials can be deduced as special cases within the framework of Schrödinger equation with mass m and potential V.…”

“…for a given potential [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. It is well known that these solutions play an essential role in the relativistic and non-relativistic quantum mechanics for some physical potentials of interest, [1,2,12,[17][18][19].…”