Analytical solutions and Herzberg's energy level for modified shifted morse molecular system.

The solution of the radial Schrödinger equation for the modified shifted Morse potential model is obtained using an approximate supersymmetric approach. The two different formulae for the computation of the centrifugal distortion constant are clearly examined to deduce the formula that gives the result that perfectly aligns with the experimental data. Numerical values for different molecules are computed for the two different values of the centrifugal distortion constant (dissociation energy) obtained from two different equations. The ground state energy spectra for different molecules are obtained using Herzberg's energy level equation as a standard for some molecules. The results of the modified shifted Morse potential are compared with the results from Herzberg's energy level equation and the experimental data. Our study reveals that the results for one of the two centrifugal distortion constants are closer to the standard results and the experimental data in all the molecules studied.