Exact analytical solutions to the Kratzer potential by the asymptotic iteration method

Abstract

For any n and l values, we present a simple exact analytical solution of the radial Schrödinger equation for the Kratzer potential within the framework of the asymptotic iteration method (AIM). The exact bound-state energy eigenvalues (E nl ) and corresponding eigenfunctions (R nl ) are calculated for various values of n and l quantum numbers for CO, NO, O 2 , and I 2 diatomic molecules.

Anyl-state solutions of the Hulthén potential by the asymptotic iteration method

“…We have shown an alternative method to obtain the energy eigenvalues and corresponding Where there is no such a solution, the energy eigenvalues are obtained by using an iterative approach [18,19,20]. As it is presented, AIM puts no constraint on the potential parameter values involved and it is easy to implement.…”

Exact quantization rule to the Kratzer-type potentials: an application to the diatomic molecules

“…Considerable interest has recently been shown in the Kratzer-Fues [12,[16][17][18][19] as a model to describe internuclear vibration of a diatomic molecule [20][21][22][23]. This potential can be expressed in the form…”

The asymptotic iteration method applied to certain quasinormal modes and non Hermitian systems

“…Recently a technique, called the Asymptotic Iteration Method (AIM) has been introduced [1,2] to obtain eigenvalues of second order homogeneous differential equations. In the case of the Schrödinger equation, it has been found that AIM exactly reproduces the energy spectrum for most exactly solvable potentials [2][3][4] and for non-exactly solvable potentials it produces very good results [5][6][7].…”