Analytical solution of the Schrödinger equation for the linear combination of the Hulthén and the class of Yukawa potentials

In this study, the bound state's solution of the modified Schrödinger equation is found for the new supposed combined Hultén potential and the Yukawa class potentials. Analytical expressions for the energy eigenvalue and the corresponding radial wave functions are obtained for any orbital quantum number. Obtained eigenfunctions are expressed in terms of hypergeometric functions. To overcome the potential's centrifugal part difficulties, we applied the developed approximation scheme for studying bound states. It is shown that energy levels and eigenfunctions are susceptible, depending on potential parameters. Finally, we investigate also the eigenvalue of the energy and the corresponding radial wave function under some exceptional cases.