Radial Solution of the S-Wave Schrodinger Equation with Kratzer Plus Modified Deng-Fan Potential Under the Framework of Nikifarov-Uvarov Method

Louis Hitler

doi:10.11648/j.ijamtp.20170304.14

Abstract

The solutions of the Schrodinger equation with Kratzer plus Modified Deng-Fan potential have been obtained using the parametric Nikiforov-Uvarov (NU) method which is based on the solutions of general second-order linear differential equations with special functions. The bound state energy eigenvalues and the corresponding un-normalized eigen functions are obtained in terms of Jacobi polynomials. Also special cases of the potential have been considered and their energyeigen values obtained.

Highlights

The exact analytic solutions of nonrelativistic and relativistic wave equations are only possible for certain potentials of physical interest
It is well known and understood that the analytical exact solutions of these wave equations are only possible in a few cases such as the harmonic oscillator, Coulomb, pseudoharmonic potentials and others [1]
The Deng-Fan molecular potential is a simple modified Morse potential called the generalized Morse potential, which was proposed by Deng and Fan in 1957 [13], in an attempt to find a more suitable diatomic potential to describe the vibrational spectrum [14]

Summary

Introduction

The exact analytic solutions of nonrelativistic and relativistic wave equations are only possible for certain potentials of physical interest. For ≠ 0approximation techniques have to be employed to deal with the centrifugal term like the Pekeris approximation [2, 3] and the approximated scheme suggested by Greene and Aldrich Some of these exponential-type potentials include the Hulthen potential [4], the Morse potential [5], the Woods-Saxon potential [3], the Kratzer-type and pseudoharmonic potentials [3, 2], the Rosen-Morse-type potentials [6], the Manning-Rosen potential [3]. The Deng-Fan molecular potential is a simple modified Morse potential called the generalized Morse potential, which was proposed by Deng and Fan in 1957 [13], in an attempt to find a more suitable diatomic potential to describe the vibrational spectrum [14] This potential is qualitatively similar to the Morse potential but it has correct asymptotic behavior as the internuclear distance approaches to zero [15].

Review of Parametric Nikifarov-Uvarov Method

Conclusion