{"id":"https://openalex.org/W7214008387","doi":"https://doi.org/10.48550/arxiv.2609.23348","title":"Field-Modified Quantum Potentials from Tridiagonal Representations: Analytical Spectra and Galerkin Simulations","display_name":"Field-Modified Quantum Potentials from Tridiagonal Representations: Analytical Spectra and Galerkin Simulations","publication_year":2026,"publication_date":"2026-09-20","ids":{"openalex":"https://openalex.org/W7214008387","doi":"https://doi.org/10.48550/arxiv.2609.23348"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.23348","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.23348","pdf_url":"https://arxiv.org/pdf/2609.23348","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"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.23348","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5150899870","display_name":"Tunde Joseph Osunmusanmi","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I176601375","display_name":"Khalifa University of Science and Technology","ror":"https://ror.org/05hffr360","country_code":"AE","type":"education","lineage":["https://openalex.org/I176601375"]}],"countries":["AE"],"is_corresponding":false,"raw_author_name":"Osunmusanmi, Tunde Joseph","raw_affiliation_strings":["College of Computing and Mathematical Sciences , Department of Applied Mathematics and Sciences , Khalifa University of Science and Technology , 127788 Abu Dhabi , United Arab Emirates"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Computing and Mathematical Sciences , Department of Applied Mathematics and Sciences , Khalifa University of Science and Technology , 127788 Abu Dhabi , United Arab Emirates","institution_ids":["https://openalex.org/I176601375"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012034002","display_name":"Berihu Teklu","orcid":"https://orcid.org/0000-0001-9280-533X","observed_orcids":["https://orcid.org/0000-0001-9280-533X"]},"institutions":[{"id":"https://openalex.org/I176601375","display_name":"Khalifa University of Science and Technology","ror":"https://ror.org/05hffr360","country_code":"AE","type":"education","lineage":["https://openalex.org/I176601375"]}],"countries":["AE"],"is_corresponding":false,"raw_author_name":"Teklu, Berihu","raw_affiliation_strings":["Center for Cyber-Physical Systems (C2PS) , Khalifa University of Science and Technology , 127788 , Abu Dhabi , United Arab Emirates","College of Computing and Mathematical Sciences , Department of Applied Mathematics and Sciences , Khalifa University of Science and Technology , 127788 Abu Dhabi , United Arab Emirates"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Cyber-Physical Systems (C2PS) , Khalifa University of Science and Technology , 127788 , Abu Dhabi , United Arab Emirates","institution_ids":["https://openalex.org/I176601375"]},{"raw_affiliation_string":"College of Computing and Mathematical Sciences , Department of Applied Mathematics and Sciences , Khalifa University of Science and Technology , 127788 Abu Dhabi , United Arab Emirates","institution_ids":["https://openalex.org/I176601375"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I176601375"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.4390000104904175,"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"}},"topics":[{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.4390000104904175,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.3546999990940094,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11262","display_name":"Quantum Mechanics and Non-Hermitian Physics","score":0.07890000194311142,"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/laguerre-basis","display_name":"Laguerre basis","score":0.8700000047683716},{"id":"https://openalex.org/keywords/meixner-pollaczek-polynomials","display_name":"Meixner-Pollaczek polynomials","score":0.9610000252723694},{"id":"https://openalex.org/keywords/meixner-polynomials","display_name":"Meixner polynomials","score":0.9710000157356262},{"id":"https://openalex.org/keywords/three-term-recurrence-relation","display_name":"three-term recurrence relation","score":0.6140000224113464}],"concepts":[{"id":"https://openalex.org/C108408018","wikidata":"https://www.wikidata.org/wiki/Q1124546","display_name":"Laguerre polynomials","level":2,"score":0.792900025844574},{"id":"https://openalex.org/C51647924","wikidata":"https://www.wikidata.org/wiki/Q1755277","display_name":"Tridiagonal matrix","level":3,"score":0.6733999848365784},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5952000021934509},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5616999864578247},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.46320000290870667},{"id":"https://openalex.org/C43475892","wikidata":"https://www.wikidata.org/wiki/Q1171964","display_name":"Laguerre's method","level":4,"score":0.46070000529289246},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.4514999985694885},{"id":"https://openalex.org/C115260700","wikidata":"https://www.wikidata.org/wiki/Q11408","display_name":"Magnetic field","level":2,"score":0.4163999855518341},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4131999909877777},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.39399999380111694},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.39309999346733093},{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.38679999113082886},{"id":"https://openalex.org/C201292218","wikidata":"https://www.wikidata.org/wiki/Q740970","display_name":"Recurrence relation","level":2,"score":0.3736000061035156},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.36410000920295715},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35370001196861267},{"id":"https://openalex.org/C63036615","wikidata":"https://www.wikidata.org/wiki/Q165498","display_name":"Schr\u00f6dinger equation","level":2,"score":0.33980000019073486},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.32260000705718994},{"id":"https://openalex.org/C4839761","wikidata":"https://www.wikidata.org/wiki/Q212111","display_name":"Spectral line","level":2,"score":0.3206999897956848},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.3206999897956848},{"id":"https://openalex.org/C48490523","wikidata":"https://www.wikidata.org/wiki/Q371631","display_name":"Jacobi polynomials","level":3,"score":0.3140999972820282},{"id":"https://openalex.org/C173523689","wikidata":"https://www.wikidata.org/wiki/Q215589","display_name":"Dipole","level":2,"score":0.31360000371932983},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.28760001063346863},{"id":"https://openalex.org/C535169671","wikidata":"https://www.wikidata.org/wiki/Q17080006","display_name":"Semiclassical physics","level":3,"score":0.2856000065803528},{"id":"https://openalex.org/C169852918","wikidata":"https://www.wikidata.org/wiki/Q390314","display_name":"Magnetic dipole","level":3,"score":0.27720001339912415},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.27619999647140503},{"id":"https://openalex.org/C58570533","wikidata":"https://www.wikidata.org/wiki/Q55451","display_name":"Electric potential","level":3,"score":0.26739999651908875},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.2671000063419342},{"id":"https://openalex.org/C96716743","wikidata":"https://www.wikidata.org/wiki/Q827688","display_name":"Poisson's equation","level":2,"score":0.2653999924659729},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.25780001282691956},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.2567000091075897},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.2535000145435333}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.23348","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.23348","pdf_url":"https://arxiv.org/pdf/2609.23348","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.2609.23348","doi":"https://doi.org/10.48550/arxiv.2609.23348","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.23348","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.23348","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.23348","pdf_url":"https://arxiv.org/pdf/2609.23348","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":[{"id":"https://openalex.org/G1094932978","display_name":null,"funder_award_id":"KU-INT-RIG-2024-8474000739","funder_id":"https://openalex.org/F4320322334","funder_display_name":"Khalifa University of Science, Technology and Research"},{"id":"https://openalex.org/G1318643119","display_name":null,"funder_award_id":"8474000739","funder_id":"https://openalex.org/F4320322334","funder_display_name":"Khalifa University of Science, Technology and Research"},{"id":"https://openalex.org/G7698709350","display_name":null,"funder_award_id":"KU-C2PS","funder_id":"https://openalex.org/F4320322334","funder_display_name":"Khalifa University of Science, Technology and Research"}],"funders":[{"id":"https://openalex.org/F4320322334","display_name":"Khalifa University of Science, Technology and Research","ror":"https://ror.org/05hffr360"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214008387.pdf","grobid_xml":"https://content.openalex.org/works/W7214008387.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7222169203","https://openalex.org/W4311248716","https://openalex.org/W2888276831","https://openalex.org/W2025529628","https://openalex.org/W2418712669","https://openalex.org/W2077130638","https://openalex.org/W2016783716","https://openalex.org/W2002311186","https://openalex.org/W6948183756","https://openalex.org/W1641042356"],"abstract_inverted_index":{"We":[0],"develop":[1],"an":[2,39],"effective":[3,154,224],"radial":[4,71,113,144],"framework":[5],"for":[6,178],"analyzing":[7],"new":[8,239],"field-modified":[9,179],"potential":[10,155,180],"function":[11],"of":[12,54,92,142,209,213,222],"a":[13,69,147,151,157,164,238,250],"charged":[14],"spinless":[15],"particle":[16],"in":[17,60,96,203,228,242],"collinear":[18],"electric":[19,49,215],"and":[20,34,51,99,111,115,123,133,156,173,190,206,212],"magnetic":[21,26,246],"fields.":[22],"Using":[23],"the":[24,31,48,52,55,61,86,97,103,106,116,130,137,140,143,184,195,198,210,214,220,223,229,232,245],"weak-":[25],"field":[27,247],"approximation,":[28],"we":[29,84],"neglect":[30],"diamagnetic":[32],"term":[33],"other":[35],"angular":[36,56],"projections":[37],"under":[38],"explicit":[40],"smallness":[41],"condition":[42],"$\\ll":[43],"\u0394E$,":[44],"where":[45],"$E$":[46],"is":[47,67,75,161,234],"field,":[50,216],"replacement":[53],"factor":[57],"by":[58],"$C=\\cos\u03b8$":[59],"spherical":[62],"coordinates.":[63],"The":[64,169],"resulting":[65],"equation":[66],"therefore":[68,128],"field-aligned":[70],"model":[72],"whose":[73],"validity":[74],"limited":[76],"to":[77,146],"angularly":[78],"localized":[79],"states.":[80],"Within":[81],"this":[82],"setting,":[83],"apply":[85],"indirect":[87],"mode":[88],"(or":[89],"search":[90],"mode)":[91],"Tridiagonal":[93],"representation":[94],"approach":[95],"Laguerre":[98,104,196],"Jacobi":[100,138,230],"bases.":[101],"In":[102,136,194],"basis,":[105,139],"tridiagonal":[107],"constraint":[108],"generates":[109],"linear-plus-inverse":[110],"linear-plus-quadratic":[112],"potentials,":[114],"coefficient":[117],"recurrences":[118],"are":[119,201,207],"connected":[120],"with":[121],"Meixner--Pollaczek":[122],"Meixner":[124],"polynomial":[125],"type":[126],"structures,":[127],"yielding":[129],"analytic":[131],"spectra":[132,200],"expansion":[134],"wavefunctions.":[135],"mapping":[141],"half-line":[145],"finite":[148],"interval":[149],"produces":[150],"singular":[152],"confining":[153],"three-term":[158,240],"recurrence":[159],"that":[160],"treated":[162],"through":[163,219,249],"truncated":[165],"generalized":[166],"eigenvalue":[167],"problem.":[168],"formulation":[170],"provides":[171],"analytically":[172],"numerically":[174,236],"tractable":[175],"benchmark":[176],"models":[177],"functions,":[181],"while":[182],"keeping":[183],"assumptions,":[185],"parameter":[186],"restrictions,":[187],"endpoint":[188],"behavior,":[189],"convergence":[191],"tests":[192],"explicit.":[193],"basis":[197,231],"resultant":[199],"obtained":[202,235],"closed":[204],"form":[205],"independent":[208],"orientation":[211],"which":[217],"enter":[218],"shape":[221],"central":[225],"potential,":[226],"whereas":[227],"spectrum":[233],"from":[237],"recurrence;":[241],"all":[243],"cases":[244],"enters":[248],"linear":[251],"Zeeman":[252],"shift.":[253]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-23T00:00:00"}
