Singular inverse square potential in coordinate space with a minimal length

Djamil Bouaziz; Tolga Birkandan

doi:10.1016/j.aop.2017.10.004

Singular inverse square potential in coordinate space with a minimal length

Djamil Bouaziz^*, Tolga Birkandan

^*Corresponding author for this work

Department of Physics Engineering

University of Jijel

Research output: Contribution to journal › Article › peer-review

29 Citations (Scopus)

Abstract

The problem of a particle of mass m in the field of the inverse-square potential α∕r² is studied in quantum mechanics with a generalized uncertainty principle, characterized by the existence of a minimal length. Using the coordinate representation, for a specific form of the generalized uncertainty relation, we solve the deformed Schrödinger equation analytically in terms of confluent Heun functions. We explicitly show the regularizing effect of the minimal length on the singularity of the potential. We discuss the problem of bound states in detail and we derive an expression for the energy spectrum in a natural way from the square integrability condition; the results are in complete agreement with the literature.

Original language	English
Pages (from-to)	62-74
Number of pages	13
Journal	Annals of Physics
Volume	387
DOIs	https://doi.org/10.1016/j.aop.2017.10.004
Publication status	Published - Dec 2017

Bibliographical note

Publisher Copyright:
© 2017 Elsevier Inc.

Funding

We thank Prof. Mahmut Hortaçsu for fruitful discussions and Prof. Michel Bawin for reading the manuscript. We also thank the referee for interesting comments and constructive criticisms that allowed us to improve the manuscript. The work of DB is supported by the Algerian Ministry of Higher Education and Scientific Research , under the CNEPRU Project No. D01720140007 . The research of TB is supported by TUBITAK, the Scientific and Technological Council of Turkey.

Funders	Funder number
Scientific and Technological Council of Turkey
TUBITAK
Ministry of Higher Education and Scientific Research

Keywords

Generalized uncertainty principle
Inverse square potential
Minimal length
Singular potential

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10.1016/j.aop.2017.10.004

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AU - Birkandan, Tolga

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AB - The problem of a particle of mass m in the field of the inverse-square potential α∕r2 is studied in quantum mechanics with a generalized uncertainty principle, characterized by the existence of a minimal length. Using the coordinate representation, for a specific form of the generalized uncertainty relation, we solve the deformed Schrödinger equation analytically in terms of confluent Heun functions. We explicitly show the regularizing effect of the minimal length on the singularity of the potential. We discuss the problem of bound states in detail and we derive an expression for the energy spectrum in a natural way from the square integrability condition; the results are in complete agreement with the literature.

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KW - Inverse square potential

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KW - Singular potential

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JO - Annals of Physics

JF - Annals of Physics

ER -

Singular inverse square potential in coordinate space with a minimal length

Abstract

Bibliographical note

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Keywords

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