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

^*Bu çalışma için yazışmadan sorumlu yazar

Fizik Mühendisliği Bölümü

University of Jijel

Araştırma sonucu: Dergiye katkı › Makale › bilirkişi

37 Atıf (Scopus)

Özet

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.

Orijinal dil	İngilizce
Sayfa (başlangıç-bitiş)	62-74
Sayfa sayısı	13
Dergi	Annals of Physics
Hacim	387
DOI'lar	https://doi.org/10.1016/j.aop.2017.10.004
Yayın durumu	Yayınlandı - Ara 2017

Bibliyografik not

Publisher Copyright:
© 2017 Elsevier Inc.

Finansman

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.

Finansörler
Scientific and Technological Council of Turkey
TUBITAK
Ministry of Higher Education and Scientific Research

Belgeye Erişim

10.1016/j.aop.2017.10.004

Diğer Dosyalar ve Linkler

Link to publication in Scopus

Alıntı Yap

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title = "Singular inverse square potential in coordinate space with a minimal length",

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 Schr{\"o}dinger 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.",

keywords = "Generalized uncertainty principle, Inverse square potential, Minimal length, Singular potential",

author = "Djamil Bouaziz and Tolga Birkandan",

note = "Publisher Copyright: {\textcopyright} 2017 Elsevier Inc.",

year = "2017",

month = dec,

doi = "10.1016/j.aop.2017.10.004",

language = "English",

volume = "387",

pages = "62--74",

journal = "Annals of Physics",

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TY - JOUR

T1 - Singular inverse square potential in coordinate space with a minimal length

AU - Bouaziz, Djamil

AU - Birkandan, Tolga

PY - 2017/12

Y1 - 2017/12

N2 - 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.

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.

KW - Generalized uncertainty principle

KW - Inverse square potential

KW - Minimal length

KW - Singular potential

UR - https://www.scopus.com/pages/publications/85033596053

U2 - 10.1016/j.aop.2017.10.004

DO - 10.1016/j.aop.2017.10.004

M3 - Article

AN - SCOPUS:85033596053

SN - 0003-4916

VL - 387

SP - 62

EP - 74

JO - Annals of Physics

JF - Annals of Physics

ER -

Singular inverse square potential in coordinate space with a minimal length

Özet

Bibliyografik not

Finansman

Belgeye Erişim

Diğer Dosyalar ve Linkler

Parmak izi

Alıntı Yap