{"id":"https://openalex.org/W2000878563","doi":"https://doi.org/10.1103/physreva.78.032110","title":"Singular inverse square potential in arbitrary dimensions with a minimal length: Application to the motion of a dipole in a cosmic string background","display_name":"Singular inverse square potential in arbitrary dimensions with a minimal length: Application to the motion of a dipole in a cosmic string background","publication_year":2008,"publication_date":"2008-09-15","ids":{"openalex":"https://openalex.org/W2000878563","doi":"https://doi.org/10.1103/physreva.78.032110","mag":"2000878563"},"language":"en","primary_location":{"id":"doi:10.1103/physreva.78.032110","doi":"https://doi.org/10.1103/physreva.78.032110","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physreva.78.032110","pdf_url":null,"source":{"id":"https://openalex.org/S164566984","display_name":"Physical Review A","issn_l":"0556-2791","issn":["0556-2791","1050-2947","1094-1622","1538-4446","2469-9926","2469-9934","2469-9942"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-a","jufo-2","ki-jl-1","norway-2","poland-100","poland-70","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review A","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1009.0930","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5047948530","display_name":"Djamil Bouaziz","orcid":"https://orcid.org/0000-0002-1541-6792","observed_orcids":["https://orcid.org/0000-0002-1541-6792"]},"institutions":[{"id":"https://openalex.org/I116970179","display_name":"University of Jijel","ror":"https://ror.org/03kkfk814","country_code":"DZ","type":"education","lineage":["https://openalex.org/I116970179"]},{"id":"https://openalex.org/I157674565","display_name":"University of Li\u00e8ge","ror":"https://ror.org/00afp2z80","country_code":"BE","type":"education","lineage":["https://openalex.org/I157674565"]}],"countries":["BE","DZ"],"is_corresponding":false,"raw_author_name":"Djamil Bouaziz","raw_affiliation_strings":["Institut de Physique B5, Universit\u00e9 de Li\u00e8ge, Sart Tilman 4000 Li\u00e8ge 1, Belgium and Laboratory of Theoretical Physics, University of Jijel, 18000, Algeria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut de Physique B5, Universit\u00e9 de Li\u00e8ge, Sart Tilman 4000 Li\u00e8ge 1, Belgium and Laboratory of Theoretical Physics, University of Jijel, 18000, Algeria","institution_ids":["https://openalex.org/I116970179","https://openalex.org/I157674565"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048484020","display_name":"Michel Bawin","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I116970179","display_name":"University of Jijel","ror":"https://ror.org/03kkfk814","country_code":"DZ","type":"education","lineage":["https://openalex.org/I116970179"]},{"id":"https://openalex.org/I157674565","display_name":"University of Li\u00e8ge","ror":"https://ror.org/00afp2z80","country_code":"BE","type":"education","lineage":["https://openalex.org/I157674565"]}],"countries":["BE","DZ"],"is_corresponding":false,"raw_author_name":"Michel Bawin","raw_affiliation_strings":["Institut de Physique B5, Universit\u00e9 de Li\u00e8ge, Sart Tilman 4000 Li\u00e8ge 1, Belgium and Laboratory of Theoretical Physics, University of Jijel, 18000, Algeria","Institut de Physique B5, Universit\u00e9 de Li\u00e8ge, Sart Tilman, 4000 Li\u00e8ge 1, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut de Physique B5, Universit\u00e9 de Li\u00e8ge, Sart Tilman 4000 Li\u00e8ge 1, Belgium and Laboratory of Theoretical Physics, University of Jijel, 18000, Algeria","institution_ids":["https://openalex.org/I116970179","https://openalex.org/I157674565"]},{"raw_affiliation_string":"Institut de Physique B5, Universit\u00e9 de Li\u00e8ge, Sart Tilman, 4000 Li\u00e8ge 1, Belgium","institution_ids":["https://openalex.org/I157674565"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2675,"currency":"USD","value_usd":2675},"apc_paid":null,"fwci":1.0307,"has_fulltext":false,"cited_by_count":54,"citation_normalized_percentile":{"value":0.7451423,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"78","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11415","display_name":"Noncommutative and Quantum Gravity Theories","score":0.8960000276565552,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11415","display_name":"Noncommutative and Quantum Gravity Theories","score":0.8960000276565552,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10025","display_name":"Black Holes and Theoretical Physics","score":0.05000000074505806,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.018799999728798866,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/inverse-square-potential","display_name":"inverse square potential","score":0.968999981880188},{"id":"https://openalex.org/keywords/minimum-length","display_name":"minimal length","score":0.9739999771118164},{"id":"https://openalex.org/keywords/heun-functions","display_name":"Heun functions","score":0.8790000081062317},{"id":"https://openalex.org/keywords/schrodinger-equation","display_name":"Schr\u00f6dinger equation","score":0.8970000147819519},{"id":"https://openalex.org/keywords/cosmic-strings","display_name":"cosmic strings","score":0.6940000057220459},{"id":"https://openalex.org/keywords/bound-states","display_name":"bound states","score":0.9150000214576721},{"id":"https://openalex.org/keywords/arbitrary-dimensions","display_name":"arbitrary dimensions","score":0.6779999732971191},{"id":"https://openalex.org/keywords/quantum-gravity","display_name":"quantum gravity","score":0.42500001192092896}],"concepts":[{"id":"https://openalex.org/C170442971","wikidata":"https://www.wikidata.org/wiki/Q1431196","display_name":"Cosmic string","level":3,"score":0.839561939239502},{"id":"https://openalex.org/C157486923","wikidata":"https://www.wikidata.org/wiki/Q1376436","display_name":"String (physics)","level":2,"score":0.7754954099655151},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.7575912475585938},{"id":"https://openalex.org/C173523689","wikidata":"https://www.wikidata.org/wiki/Q215589","display_name":"Dipole","level":2,"score":0.7031832933425903},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.6835465431213379},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5673491358757019},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.5491469502449036},{"id":"https://openalex.org/C174084160","wikidata":"https://www.wikidata.org/wiki/Q908049","display_name":"Bound state","level":2,"score":0.4473136365413666},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.4304896295070648},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.4159952402114868},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.38343679904937744},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3661447763442993},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.21230503916740417},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2081581950187683},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1103/physreva.78.032110","doi":"https://doi.org/10.1103/physreva.78.032110","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physreva.78.032110","pdf_url":null,"source":{"id":"https://openalex.org/S164566984","display_name":"Physical Review A","issn_l":"0556-2791","issn":["0556-2791","1050-2947","1094-1622","1538-4446","2469-9926","2469-9934","2469-9942"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-a","jufo-2","ki-jl-1","norway-2","poland-100","poland-70","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review A","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1009.0930","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1009.0930","pdf_url":"https://arxiv.org/pdf/1009.0930","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.1009.0930","doi":"https://doi.org/10.48550/arxiv.1009.0930","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1009.0930","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1009.0930","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1009.0930","pdf_url":"https://arxiv.org/pdf/1009.0930","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":64,"referenced_works":["https://openalex.org/W6734664","https://openalex.org/W60675102","https://openalex.org/W1606337696","https://openalex.org/W1800127362","https://openalex.org/W1967353827","https://openalex.org/W1973249358","https://openalex.org/W1975850914","https://openalex.org/W1978154760","https://openalex.org/W1979455551","https://openalex.org/W1983292754","https://openalex.org/W1986421223","https://openalex.org/W1987581139","https://openalex.org/W1988028632","https://openalex.org/W1988850063","https://openalex.org/W1989104288","https://openalex.org/W1989919448","https://openalex.org/W1989928886","https://openalex.org/W1990532383","https://openalex.org/W1998751468","https://openalex.org/W2000542101","https://openalex.org/W2003813466","https://openalex.org/W2004666616","https://openalex.org/W2004842157","https://openalex.org/W2009037511","https://openalex.org/W2011260669","https://openalex.org/W2014764013","https://openalex.org/W2017393308","https://openalex.org/W2021311856","https://openalex.org/W2024106644","https://openalex.org/W2027783061","https://openalex.org/W2036028280","https://openalex.org/W2036964921","https://openalex.org/W2038003015","https://openalex.org/W2038739505","https://openalex.org/W2038909469","https://openalex.org/W2039129614","https://openalex.org/W2050176365","https://openalex.org/W2051763640","https://openalex.org/W2054924364","https://openalex.org/W2057466582","https://openalex.org/W2063670249","https://openalex.org/W2074453870","https://openalex.org/W2080603361","https://openalex.org/W2080818260","https://openalex.org/W2082981643","https://openalex.org/W2086615228","https://openalex.org/W2091839795","https://openalex.org/W2096960957","https://openalex.org/W2111216105","https://openalex.org/W2127995081","https://openalex.org/W2133635683","https://openalex.org/W2142397325","https://openalex.org/W2142768579","https://openalex.org/W2147264052","https://openalex.org/W2148365462","https://openalex.org/W2150611802","https://openalex.org/W2166052619","https://openalex.org/W2170399496","https://openalex.org/W2178245300","https://openalex.org/W2257133510","https://openalex.org/W2801179766","https://openalex.org/W3098137474","https://openalex.org/W4211108802","https://openalex.org/W4234941667"],"related_works":["https://openalex.org/W2763468061","https://openalex.org/W2091839795","https://openalex.org/W1710947744","https://openalex.org/W2609722747","https://openalex.org/W2008348139","https://openalex.org/W2150611802","https://openalex.org/W1992480794","https://openalex.org/W3121042390","https://openalex.org/W2078185271","https://openalex.org/W2071534214"],"abstract_inverted_index":{"We":[0,24,39,61],"solve":[1],"analytically":[2],"the":[3,7,29,48,51,55,70,82],"Schr\\\"odinger":[4],"equation":[5],"for":[6],"$N$-dimensional":[8],"inverse":[9],"square":[10],"potential":[11],"in":[12,19,34,69],"quantum":[13],"mechanics":[14],"with":[15,65],"a":[16,32,35,42,79],"minimal":[17,73],"length":[18,74],"terms":[20],"of":[21,31,81],"Heun's":[22],"functions.":[23],"apply":[25],"our":[26,63],"results":[27,64],"to":[28],"problem":[30],"dipole":[33,52],"cosmic":[36,83],"string":[37,56],"background.":[38],"find":[40],"that":[41],"bound":[43],"state":[44],"exists":[45],"only":[46],"if":[47],"angle":[49],"between":[50],"moment":[53],"and":[54],"is":[57],"larger":[58],"than":[59],"$\\ensuremath{\\pi}\u22154$.":[60],"compare":[62],"recent":[66],"conflicting":[67],"conclusions":[68],"literature.":[71],"The":[72],"may":[75],"be":[76],"interpreted":[77],"as":[78],"radius":[80],"string.":[84]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":8},{"year":2012,"cited_by_count":3}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2016-06-24T00:00:00"}