### 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 S_{0}(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 language | English |
---|---|

Pages (from-to) | 1936-1942 |

Number of pages | 7 |

Journal | Physics Letters, Section A: General, Atomic and Solid State Physics |

Volume | 381 |

Issue number | 23 |

DOIs | |

Publication status | Published - Jun 21 2017 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Physics Letters, Section A: General, Atomic and Solid State Physics*,

*381*(23), 1936-1942. https://doi.org/10.1016/j.physleta.2017.04.010

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

Research output: Contribution to journal › Article

*Physics Letters, Section A: General, Atomic and Solid State Physics*, vol. 381, no. 23, pp. 1936-1942. https://doi.org/10.1016/j.physleta.2017.04.010

}

TY - JOUR

T1 - Analytical solutions for the radial Scarf II potential

AU - Lévai, G.

AU - Baran,

AU - Salamon, P.

AU - Vertse, T.

PY - 2017/6/21

Y1 - 2017/6/21

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.

AB - 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.

KW - Analytical solutions

KW - Bound states

KW - Radial potentials

KW - Resonances

KW - S-matrix

KW - Scarf II potential

UR - http://www.scopus.com/inward/record.url?scp=85017453988&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85017453988&partnerID=8YFLogxK

U2 - 10.1016/j.physleta.2017.04.010

DO - 10.1016/j.physleta.2017.04.010

M3 - Article

VL - 381

SP - 1936

EP - 1942

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

IS - 23

ER -