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TMF, 2018, Volume 195, Number 3, Pages 422–436 (Mi tmf9445)  

This article is cited in 2 scientific papers (total in 2 papers)

Four-parameter $1/r^2$ singular short-range potential with rich bound states and a resonance spectrum

A. D. Alhaidari

Saudi Center for Theoretical Physics, Jeddah, Saudi Arabia

Abstract: We use the tridiagonal representation approach to enlarge the class of exactly solvable quantum systems. For this, we use a square-integrable basis in which the matrix representation of the wave operator is tridiagonal. In this case, the wave equation becomes a three-term recurrence relation for the expansion coefficients of the wave function with a solution in terms of orthogonal polynomials that is equivalent to a solution of the original problem. We obtain S-wave bound states for a new four-parameter potential with a $1/r^2$ singularity but short-range, which has an elaborate configuration structure and rich spectral properties. A particle scattered by this potential must overcome a barrier and can then be trapped in the potential valley in a resonance or bound state. Using complex rotation, we demonstrate the rich spectral properties of the potential in the case of a nonzero angular momentum and show how this structure varies with the parameters of the potential.

Keywords: $1/r^2$ singular potential, tridiagonal representation, recurrence relation, parameter spectrum, bound state, resonance.

DOI: https://doi.org/10.4213/tmf9445

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English version:
Theoretical and Mathematical Physics, 2018, 195:3, 861–873

Bibliographic databases:

Document Type: Article
PACS: 03.65.Ge, 03.65.Fd, 34.80.Bm, 03.65.Ca
Received: 10.08.2017
Revised: 04.09.2017

Citation: A. D. Alhaidari, “Four-parameter $1/r^2$ singular short-range potential with rich bound states and a resonance spectrum”, TMF, 195:3 (2018), 422–436; Theoret. and Math. Phys., 195:3 (2018), 861–873

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Alhaidari A.D., “Series Solutions of Laguerre- and Jacobi-Type Differential Equations in Terms of Orthogonal Polynomials and Physical Applications”, J. Math. Phys., 59:6 (2018), 063508  crossref  isi
    2. Assi I.A., Bahlouli H., Hamdan A., “Exact Solvability of Two New 3D and 1D Non-Relativistic Potentials Within the Tra Framework”, Mod. Phys. Lett. A, 33:32 (2018), 1850187  crossref  mathscinet  zmath  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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