Introducing a new family of short-range potentials and their numerical solutions using the asymptotic iteration method
Department of Physics and Physical Oceanography, Memorial University of Newfoundland, A1B 3X7, St. John’s, NL, Canada
2 Faculty of Technology and Applied Sciences, Al-Quds Open University, Nablus, Palestine
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Accepted: 3 April 2018
Published online: 7 May 2018
The goal of this work is to derive a new class of short-range potentials that could have a wide range of physical applications, specially in molecular physics. The tridiagonal representation approach has been developed beyond its limitations to produce new potentials by requiring the representation of the Schrödinger wave operator to be multidiagonal and symmetric. This produces a family of Hulthén potentials that has a specific structure, as mentioned in the introduction. As an example, we have solved the nonrelativistic wave equation for the new four-parameter short-range screening potential numerically using the asymptotic iteration method, where we tabulated the eigenvalues for both s -wave and arbitrary l -wave cases in tables.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2018