Analytical solutions for the radial Scarf II potential

G. Lévai, Baran, P. Salamon, T. Vertse

Research output: Contribution to journalArticle

Abstract

The real Scarf II potential is discussed as a radial problem. This potential has been studied extensively as a one-dimensional problem, and now these results are used to construct its bound and resonance solutions for l=0 by setting the origin at some arbitrary value of the coordinate. The solutions with appropriate boundary conditions are composed as the linear combination of the two independent solutions of the Schrödinger equation. The asymptotic expression of these solutions is used to construct the S0(k) s-wave S-matrix, the poles of which supply the k values corresponding to the bound, resonance and anti-bound solutions. The location of the discrete energy eigenvalues is analyzed, and the relation of the solutions of the radial and one-dimensional Scarf II potentials is discussed. It is shown that the generalized Woods–Saxon potential can be generated from the Rosen–Morse II potential in the same way as the radial Scarf II potential is obtained from its one-dimensional correspondent. Based on this analogy, possible applications are also pointed out.

Original languageEnglish
Pages (from-to)1936-1942
Number of pages7
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Volume381
Issue number23
DOIs
Publication statusPublished - Jun 21 2017

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eigenvalues
poles
boundary conditions
matrices
energy

Keywords

  • Analytical solutions
  • Bound states
  • Radial potentials
  • Resonances
  • S-matrix
  • Scarf II potential

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Analytical solutions for the radial Scarf II potential. / Lévai, G.; Baran; Salamon, P.; Vertse, T.

In: Physics Letters, Section A: General, Atomic and Solid State Physics, Vol. 381, No. 23, 21.06.2017, p. 1936-1942.

Research output: Contribution to journalArticle

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N2 - The real Scarf II potential is discussed as a radial problem. This potential has been studied extensively as a one-dimensional problem, and now these results are used to construct its bound and resonance solutions for l=0 by setting the origin at some arbitrary value of the coordinate. The solutions with appropriate boundary conditions are composed as the linear combination of the two independent solutions of the Schrödinger equation. The asymptotic expression of these solutions is used to construct the S0(k) s-wave S-matrix, the poles of which supply the k values corresponding to the bound, resonance and anti-bound solutions. The location of the discrete energy eigenvalues is analyzed, and the relation of the solutions of the radial and one-dimensional Scarf II potentials is discussed. It is shown that the generalized Woods–Saxon potential can be generated from the Rosen–Morse II potential in the same way as the radial Scarf II potential is obtained from its one-dimensional correspondent. Based on this analogy, possible applications are also pointed out.

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