EIGENSOLUTIONS AND THERMODYNAMIC PROPERTIES OF THEECKARTPLUSHULTHÉN POTENTIALANDACLASSOF YUKAWA

Abstract

In this paper, we present the bound-state solutions of the Schrödinger equation and analyze the thermodynamic properties of the Eckart plus Hulthén potential and a class of Yukawa potentials. The eigenvalues and eigenfunctions were determined using the Parametric Nikiforov-Uvarov Method (PNUM). The eigenenergies of HCl and ScH molecules were calculated for various values of n and ℓ. All calculated eigenenergies for these molecules are negative, unlike those in atomic units. For a given pair (n, ℓ), the energy of ScH is higher than that of HCl. Furthermore, for these molecules, at constant n, the energy increases with increasing ℓ; and at constant ℓ, the energy increases with increasing n. The obtained energy values were then used to calculate the partition function, which served as a basis to derive thermodynamic properties such as mean energy, specific heat capacity, entropy, and free energy. The study revealed that the system exhibits high disorder for small values of β, while increasing β leads to a significant reduction in disorder.