Introducing a new family of short-range potentials and their numerical solutions using the asymptotic iteration method
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.
- 1.F. Cooper, A. Khare, U. Sukhatme, Supersymmetry in Quantum Mechanics (World Scientific, Singapore, 2001)Google Scholar
- 2.D.J. Griffiths, Introduction to Quantum Mechanics (Cambridge University Press, 2016)Google Scholar
- 3.C. Cohen-Tannoudji, B. Diu, F. Laloe, Quantum Mechanics, Vol. 1 (Wiley, New York, 1977) pp. 315--328Google Scholar
- 8.A.F. Nikiforov, V.B. Uvarov, Special Functions of Mathematical Physics (Birkhauser, Basel, 1988)Google Scholar
- 22.R. Koekoek, R.F. Swarttouw, The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue, arXiv:math/9602214 [math. CA]Google Scholar
- 23.G.B. Arfken, H.J. Weber, Mathematical Methods for Physicists (Elsevier, 1999)Google Scholar