RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
 General information Latest issue Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 TMF: Year: Volume: Issue: Page: Find

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

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

Full text: PDF file (531 kB)
First page: PDF file
References: PDF file   HTML file

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
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
\Bibitem{Alh18}
\by A.~D.~Alhaidari
\paper Four-parameter $1/r^2$ singular short-range potential with rich bound states and a~resonance spectrum
\jour TMF
\yr 2018
\vol 195
\issue 3
\pages 422--436
\mathnet{http://mi.mathnet.ru/tmf9445}
\crossref{https://doi.org/10.4213/tmf9445}
\elib{http://elibrary.ru/item.asp?id=34940707}
\transl
\jour Theoret. and Math. Phys.
\yr 2018
\vol 195
\issue 3
\pages 861--873
\crossref{https://doi.org/10.1134/S0040577918060053}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85048785755}

• http://mi.mathnet.ru/eng/tmf9445
• https://doi.org/10.4213/tmf9445
• http://mi.mathnet.ru/eng/tmf/v195/i3/p422

 SHARE:

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
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
•  Number of views: This page: 81 References: 12 First page: 5