Exact Quantization Rule to the Kratzer-Type Potentials: An Application to the Diatomic Molecules

Abstract

For any arbitrary values of $n$ and $l$ quantum numbers, we present a simple exact analytical solution of the $D$-dimensional ($D\ge 2$) hyperradial Schr% ödinger equation with the Kratzer and the modified Kratzer potentials within the framework of the exact quantization rule (EQR) method. The exact energy levels $(E_{nl})$ of all the bound-states are easily calculated from this EQR method. The corresponding normalized hyperradial wave functions are also calculated. The exact energy eigenvalues for these Kratzer-type potentials are calculated numerically for the typical diatomic molecules $LiH,$ $CH,$ $HCl,$ $CO,$ $NO,$ $O_2,$ $N_2$ and $I_2$ for various values of $n$ and $l$ quantum numbers. Numerical tests using the energy calculations for the interdimensional degeneracy ($D=2-4$) for $I_2,$ $LiH,$ $HCl,$ $O_2,$ $NO$ and $CO$ are also given. Our results obtained by EQR are in exact agreement with those obtained by other methods.

26 pages

References in corpus (3)

• Approximate l-state solutions of the D-dimensional Schrodinger equation for Manning-Rosen potential
• Relativistic treatment in D-dimensions to a spin-zero particle with noncentral equal scalar and vector ring-shaped Kratzer potential
• Approximate l-state solutions of the Manning-Rosen potential by the Nikiforov-Uvarov method