Abstract
We present the bound state solutions of the Schr\"odinger equation with generalized inverted hyperbolic potential using the Nikiforov-Uvarov method. We obtain the energy spectrum and the wave function with this potential for arbitrary - state. We show that the results of this potential reduced to the standard known potentials - Rosen-Morse, Poschl - Teller and Scarf potential as special cases. We also discussed the energy equation and the wave function for these special cases.
Highlights
The analytical and numerical solutions of the wave equations for both relativistic and non-relativistic cases have taken a great deal of interest recently
The present paper is an attempt to carry out the analytical solutions of the Schrodinger equation with the generalized inverted hyperbolic potential using the Nikiforov-Uvarov method (NU) method
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
Summary
The analytical and numerical solutions of the wave equations for both relativistic and non-relativistic cases have taken a great deal of interest recently. We aim to solve the radial Schrödinger equation for quantum mechanical system with inverted generalized hyperbolic potential and show the results for this potential using Nikiforov-Uvarov method (NU), [20]. The present paper is an attempt to carry out the analytical solutions of the Schrodinger equation with the generalized inverted hyperbolic potential using the NU method. The hyperbolic potentials under investigations are commonly used to model inter-atomic and intermolecular forces [10,21] 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].
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