Abstract
The arbitrary angular momentum solutions of the Schrödinger equation for a diatomic molecule with the general exponential screened coulomb potential of the form V(r) = (− a / r){1+ (1+ br )e−2br } has been presented. The energy eigenvalues and the corresponding eigenfunctions are calculated analytically by the use of Nikiforov-Uvarov (NU) method which is related to the solutions in terms of Jacobi polynomials. The bounded state eigenvalues are calculated numerically for the 1s state of N2 CO and NO.
Highlights
The exact analytic solutions of the wave equations are only possible for certain potentials of physical interest under consideration since they contain all the necessary information on the quantum system [1]
A more general exponential screened coulomb (MGESC) potential used in this paper is of the form [6]: V(r) = ⎜⎛ − a ⎟⎞{1+ (1+ br )exp(− 2br )}
We have decided to explore the possibility of using it in obtaining bound state solutions of the Schrödinger equation for diatomics using Nikiforov-Uvarov (NU) method
Summary
The exact analytic solutions of the wave equations (non-relativistic and relativistic) are only possible for certain potentials of physical interest under consideration since they contain all the necessary information on the quantum system [1]. In some cases, like for the ≠ 0 states, some approximations are often used to obtain analytic solutions of the Schrödinger equation [3 – 5]. We have decided to explore the possibility of using it in obtaining bound state solutions of the Schrödinger equation for diatomics using Nikiforov-Uvarov (NU) method. The NU method is based on the solutions of general second order linear differential equations with some orthogonal functions [7].
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