{"id":"https://openalex.org/W2139339502","doi":"https://doi.org/10.1063/1.529328","title":"Shift operators for a Dirac oscillator","display_name":"Shift operators for a Dirac oscillator","publication_year":1991,"publication_date":"1991-05-01","ids":{"openalex":"https://openalex.org/W2139339502","doi":"https://doi.org/10.1063/1.529328","mag":"2139339502"},"language":"en","primary_location":{"id":"doi:10.1063/1.529328","doi":"https://doi.org/10.1063/1.529328","is_oa":false,"landing_page_url":"https://doi.org/10.1063/1.529328","pdf_url":null,"source":{"id":"https://openalex.org/S158241587","display_name":"Journal of Mathematical Physics","issn_l":"0022-2488","issn":["0022-2488","1089-7658","1527-2427"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-c","jufo-1","norway-1","poland-70","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310320257","host_organization_name":"American Institute of Physics","host_organization_lineage":["https://openalex.org/P4310320257"],"host_organization_lineage_names":["American Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Physics","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5084619417","display_name":"Owen L. de Lange","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I95023434","display_name":"University of KwaZulu-Natal","ror":"https://ror.org/04qzfn040","country_code":"ZA","type":"education","lineage":["https://openalex.org/I95023434"]}],"countries":["ZA"],"is_corresponding":true,"raw_author_name":"O. L. de Lange","raw_affiliation_strings":["Physics Department, University of Natal, P.O. Box 375, Pietermaritzburg 3200, South Africa"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Physics Department, University of Natal, P.O. Box 375, Pietermaritzburg 3200, South Africa","institution_ids":["https://openalex.org/I95023434"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5084619417"],"corresponding_institution_ids":["https://openalex.org/I95023434"],"apc_list":null,"apc_paid":null,"fwci":0.2284,"has_fulltext":false,"cited_by_count":31,"citation_normalized_percentile":{"value":0.52798426,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"32","issue":"5","first_page":"1296","last_page":"1300"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11262","display_name":"Quantum Mechanics and Non-Hermitian Physics","score":0.6596999764442444,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/T11262","display_name":"Quantum Mechanics and Non-Hermitian Physics","score":0.6596999764442444,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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":0.1785999983549118,"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"}},{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.033900000154972076,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/dirac-oscillator","display_name":"Dirac oscillator","score":0.8759999871253967},{"id":"https://openalex.org/keywords/shift-operator","display_name":"shift operator","score":0.9990000128746033},{"id":"https://openalex.org/keywords/energy-eigenvalues","display_name":"energy eigenvalues","score":0.859000027179718},{"id":"https://openalex.org/keywords/expectation-values","display_name":"expectation values","score":0.8949999809265137},{"id":"https://openalex.org/keywords/matrix-elements","display_name":"matrix elements","score":0.9639999866485596},{"id":"https://openalex.org/keywords/algebraic-methods","display_name":"algebraic methods","score":0.7559999823570251}],"concepts":[{"id":"https://openalex.org/C149545384","wikidata":"https://www.wikidata.org/wiki/Q5280160","display_name":"Dirac algebra","level":3,"score":0.7009355425834656},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6391797661781311},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.5730639100074768},{"id":"https://openalex.org/C177547823","wikidata":"https://www.wikidata.org/wiki/Q5133083","display_name":"Clifford analysis","level":3,"score":0.5695115327835083},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5504964590072632},{"id":"https://openalex.org/C82601208","wikidata":"https://www.wikidata.org/wiki/Q272621","display_name":"Dirac equation","level":2,"score":0.538722038269043},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5260263085365295},{"id":"https://openalex.org/C50953366","wikidata":"https://www.wikidata.org/wiki/Q385599","display_name":"Dirac comb","level":5,"score":0.5242357850074768},{"id":"https://openalex.org/C61039578","wikidata":"https://www.wikidata.org/wiki/Q604279","display_name":"Dirac (video compression format)","level":3,"score":0.504231333732605},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.49230682849884033},{"id":"https://openalex.org/C134440745","wikidata":"https://www.wikidata.org/wiki/Q1186765","display_name":"Ladder operator","level":4,"score":0.48600897192955017},{"id":"https://openalex.org/C158650840","wikidata":"https://www.wikidata.org/wiki/Q907439","display_name":"Dirac operator","level":2,"score":0.4512372314929962},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.43185558915138245},{"id":"https://openalex.org/C156785651","wikidata":"https://www.wikidata.org/wiki/Q688945","display_name":"Dirac spinor","level":4,"score":0.42846834659576416},{"id":"https://openalex.org/C113603373","wikidata":"https://www.wikidata.org/wiki/Q2362761","display_name":"Wave function","level":2,"score":0.42609071731567383},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.41122862696647644},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3710077702999115},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3592339754104614},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.35432112216949463},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.3301225006580353},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.292031466960907},{"id":"https://openalex.org/C79013869","wikidata":"https://www.wikidata.org/wiki/Q1780743","display_name":"Compact operator","level":3,"score":0.11971330642700195},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0745091438293457},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.0},{"id":"https://openalex.org/C186453547","wikidata":"https://www.wikidata.org/wiki/Q2126","display_name":"Neutrino","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1063/1.529328","doi":"https://doi.org/10.1063/1.529328","is_oa":false,"landing_page_url":"https://doi.org/10.1063/1.529328","pdf_url":null,"source":{"id":"https://openalex.org/S158241587","display_name":"Journal of Mathematical Physics","issn_l":"0022-2488","issn":["0022-2488","1089-7658","1527-2427"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-c","jufo-1","norway-1","poland-70","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310320257","host_organization_name":"American Institute of Physics","host_organization_lineage":["https://openalex.org/P4310320257"],"host_organization_lineage_names":["American Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Physics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[{"score":0.8199999928474426,"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1982865920","https://openalex.org/W1984220188","https://openalex.org/W1995250829","https://openalex.org/W2000566946","https://openalex.org/W2010785223","https://openalex.org/W2028785431","https://openalex.org/W2035138465","https://openalex.org/W2042076331","https://openalex.org/W2058834119","https://openalex.org/W2155051947","https://openalex.org/W2167076377"],"related_works":["https://openalex.org/W3103963581","https://openalex.org/W2010571903","https://openalex.org/W2035100057","https://openalex.org/W3151684755","https://openalex.org/W190423193","https://openalex.org/W1998400122","https://openalex.org/W842170609","https://openalex.org/W2069691161","https://openalex.org/W2170109729","https://openalex.org/W2099438527"],"abstract_inverted_index":{"Shift":[0],"operators":[1,9],"are":[2,14],"obtained":[3],"for":[4],"a":[5],"Dirac":[6],"oscillator.":[7],"These":[8],"and":[10,20,26],"other":[11],"algebraic":[12],"methods":[13],"used":[15],"to":[16],"determine":[17],"energy":[18],"eigenvalues":[19],"eigenkets,":[21],"expectation":[22],"values,":[23],"matrix":[24],"elements,":[25],"coordinate-space":[27],"wave":[28],"functions.":[29]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-10-14T16:39:01.820549","created_date":"2025-10-10T00:00:00"}
