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

For arbitrary values of n and l quantum numbers, we present a simple exact analytical solution of the D-dimensional (D a parts per thousand yen 2) hyperradial Schrodinger equation with the Kratzer and the modified Kratzer potentials within the framework of the exact quantization rule (EQR) method. The exact bound state energy eigenvalues (E (nl) ) are easily calculated from this EQR method. The corresponding normalized hyperradial wave functions (psi (nl) (r)) are also calculated. The exact energy eigenvalues for these Kratzer-type potentials are calculated numerically for a few typical LiH, CH, HCl, CO, NO, O-2, N-2 and I-2 diatomic molecules for various values of n and l quantum numbers. Numerical tests using the energy calculations for the inter dimensional 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.