Molecular spinless energies of the modified Rosen–Morse potential energy model in higher spatial dimensions

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.

Relativistic spectral bounds for the general molecular potential: application to a diatomic molecule

We tackle with the Dirac equation in the presence of the general molecular potential (GMP). The spin symmetric solution of the relativistic wave equation is obtained by considering the Pekeris-type approximation scheme to deal with the centrifugal term, and in order to solve second-order differential equation, the asymptotic iteration method (AIM) is used. The closed form of the energy eigenvalue equation is found out for any values of the angular momentum quantum number. We calculate the relativistic vibrational bound state energies of 5¹Δ_g state of Na₂ molecule and compare them with the Rydberg-Klein-Rees (RKR) data. We show that relativistic vibrational energies of this molecule, which are found in the spin symmetric case, are more convenient with experimental RKR data than non-relativistic vibrational energies. We also obtain normalization constant by considering inductive approach and investigate the radial eigenfunctions and probability density functions corresponding to different eigenvalues graphically for the Na₂(5¹Δ_g) molecule.