Eigensolutions, scattering phase shift and thermodynamic properties ofHulthẻn-Yukawa potential

The amendibility of a spin-0 and spin-1 particle with a combined potential in the presence of the Duffin-Kemmer-Petiau wave equation is highly recommendable. Thus, the approximate bound state of the Duffin-Kemmer-Petiauequation and Schrӧdinger equation were obtained with a combination of Hulthẻn and Yukawa potentials in theframework of asymptotic iteration method and parametric Nikiforov-Uvarov method respectively for any ar-bitrary angular momentum quantum numberJusing a suitable approximate scheme to the centrifugal term. Thiswas done when the second-order homogeneous differential equation was transformed to a form of recurrencerelation from which a quantization condition obtained was used to calculate the eigenvalue energy equation andthe corresponding wave function. In other to apply more application to this work, the scattering phase shift ofthe Duffin-Kemmer-Petiau equation was calculated and the thermodynamic properties of the potential underconsideration were also calculated in view of the Schrӧdinger equation. It is noted that the results obtained byvarying the two strengths of the potential differs due to the effect of the screening parameter