Direct approach to bound-state solutions of the Yukawa potential

Abstract

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.

Keywords:

• screened Coulomb potential
• point canonical transformation
• Schrödinger equation, exponential-type potentials
• bound-states solutions

PACS:

• 0.365Ge
• 03.65.Fd
• 03.65Ca

Acknowledgements

J. García-Martínez acknowledges the IPN-ESFM, for the hospitality during his PhD studies in Science and Technology. We are grateful with the SNI – Conacyt – Mexico, for the stipend received.

Additional information

Funding

This work was partially supported by the projects UAM-A-CBI-2232004 and 009, under the responsibility of J. Morales and J.J. Peña respectively. J. García-Ravelo thanks the Instituto Politécnico Nacional for the financial support given through the COFAA-IPN project SIP-20141465.