Direct approach to bound-state solutions of the Yukawa potential

In this work, a straightforward approach to finding bound-state solutions of the Yukawa potential is presented. The proposal essentially converts the Schrödinger equation into a hypergeometric differential equation by means of a coordinate transformation together with a function transformation with the aim of finding the bound-state solutions of the multiparameter exponential-type potentials. The usefulness of the proposal is shown with the study of the bound-state solutions of the Yukawa potential in the frame of the Green and Aldrich approximation to the centrifugal term. Besides that the proposal is by far simpler than procedures developed with the same purpose, our algorithm accepts other kind of approximations to the 1/r² term as well as the treatment of other specific exponential potentials, which can be obtained using a proper selection of the involved parameters. That is, instead of studying a given exponential-type potential with a specialised method, the energy spectra and wavefunctions are directly obtained as a particular case from the proposal.