Thermal and atomic properties of hydrogen atom and diatomic molecules in Wilson-Racah Quantum System

In this study, a conventional quantum mechanics in which the potential function is not specified but replaced by specifying four parameters Wilson-Racah orthogonal polynomials in the energy and physical parameter space was presented. The wave function is written as a bounded sum of elements of a complete basis with these polynomials as expansion coefficients. By finding the asymptotic of these Wilson – Racah polynomials, the physical properties of the corresponding system (wave function, bound state energy spectrum and/or scattering phase shift) was obtained. Wilson – Racah quantum system was applied to determine the thermodynamics and atomic properties of Hydrogen atom and diatomic molecules. All properties of associated physical systems are obtained directly and simply from the asymptotic of the associated orthogonal polynomials. This new model, gives good an approximate prediction of the Hydrogen atom energy with an estimated average error of 0.125%. The proposed procedure merely relies on experimental values of five molecular constants. The average relative percentage deviations of the thermodynamic properties’ functions Q, U, C, S and F which are 2.42, 0.45, 0.30, 1.23 and 1.50% satisfied the experimental finding as ascertained. These represent satisfactory compromise between accuracy and rapid computations.