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

For any arbitrary values of n and l quantum numbers, we present a simple exact analytical solution of the D-dimensional (D ≥ 2) hyperradial Schrödinger equation with the Kratzer and the modified Kratzer potentials within the framework of the exact quantization rule (EQR) method. The exact energy levels (Enl) of all the bound-states are easily calculated from this EQR method. The corresponding normalized hyperradial wave functions (ψnl(r)) 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, O2, N2 and I2 for various values of n and l quantum numbers. Numerical tests using the energy calculations for the interdimensional degeneracy (D = 2 − 4) for I2, LiH, HCl, O2, NO and CO are also given. Our results obtained by EQR are in exact agreement with those obtained by other methods.