Eigensolutions, scattering phase shift and thermodynamic properties of Hulthẻn-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-Petiau equation and Schrӧdinger equation were obtained with a combination of Hulthẻn and Yukawa potentials in the framework of asymptotic iteration method and parametric Nikiforov-Uvarov method respectively for any arbitrary angular momentum quantum number J using a suitable approximate scheme to the centrifugal term. This was done when the second-order homogeneous differential equation was transformed to a form of recurrence relation from which a quantization condition obtained was used to calculate the eigenvalue energy equation and the corresponding wave function. In other to apply more application to this work, the scattering phase shift of the Duffin-Kemmer-Petiau equation was calculated and the thermodynamic properties of the potential under consideration were also calculated in view of the Schrӧdinger equation. It is noted that the results obtained by varying the two strengths of the potential differs due to the effect of the screening parameter. Keywords: Bound state, Wave equation, Eigensolutions, Scattering state, Phase shift, Thermodynamic properties