{"id":"https://openalex.org/W1985994523","doi":"https://doi.org/10.1088/1751-8113/46/8/085303","title":"Determination of resonances by the optimized spectral approach","display_name":"Determination of resonances by the optimized spectral approach","publication_year":2013,"publication_date":"2013-02-08","ids":{"openalex":"https://openalex.org/W1985994523","doi":"https://doi.org/10.1088/1751-8113/46/8/085303","mag":"1985994523"},"language":"en","primary_location":{"id":"doi:10.1088/1751-8113/46/8/085303","doi":"https://doi.org/10.1088/1751-8113/46/8/085303","is_oa":true,"landing_page_url":"https://doi.org/10.1088/1751-8113/46/8/085303","pdf_url":"https://iopscience.iop.org/article/10.1088/1751-8113/46/8/085303/pdf","source":{"id":"https://openalex.org/S79244937","display_name":"Journal of Physics A Mathematical and Theoretical","issn_l":"1751-8113","issn":["1751-8113","1751-8121"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-2","norway-1","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310311669","host_organization_name":"Institute of Physics","host_organization_lineage":["https://openalex.org/P4310311669"],"host_organization_lineage_names":["Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Physics A: Mathematical and Theoretical","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://iopscience.iop.org/article/10.1088/1751-8113/46/8/085303/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030579100","display_name":"Arkadiusz Kuro\u015b","orcid":"https://orcid.org/0000-0002-3448-4037","observed_orcids":["https://orcid.org/0000-0002-3448-4037"]},"institutions":[{"id":"https://openalex.org/I169495764","display_name":"Jan Kochanowski University","ror":"https://ror.org/00krbh354","country_code":"PL","type":"education","lineage":["https://openalex.org/I169495764"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Arkadiusz Kuro\u015b","raw_affiliation_strings":["Institute of Physics, Jan Kochanowski University, \u015awie\u00b8tokrzyska 15, 25-406 Kielce, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Physics, Jan Kochanowski University, \u015awie\u00b8tokrzyska 15, 25-406 Kielce, Poland","institution_ids":["https://openalex.org/I169495764"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043977180","display_name":"Przemys\u0142aw Ko\u015bcik","orcid":"https://orcid.org/0000-0001-7926-7522","observed_orcids":["https://orcid.org/0000-0001-7926-7522"]},"institutions":[{"id":"https://openalex.org/I169495764","display_name":"Jan Kochanowski University","ror":"https://ror.org/00krbh354","country_code":"PL","type":"education","lineage":["https://openalex.org/I169495764"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Przemys\u0142aw Ko\u015bcik","raw_affiliation_strings":["Institute of Physics, Jan Kochanowski University, \u015awie\u00b8tokrzyska 15, 25-406 Kielce, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Physics, Jan Kochanowski University, \u015awie\u00b8tokrzyska 15, 25-406 Kielce, Poland","institution_ids":["https://openalex.org/I169495764"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050544368","display_name":"Anna Okopi\u0144ska","orcid":"https://orcid.org/0000-0003-4601-913X","observed_orcids":["https://orcid.org/0000-0003-4601-913X"]},"institutions":[{"id":"https://openalex.org/I169495764","display_name":"Jan Kochanowski University","ror":"https://ror.org/00krbh354","country_code":"PL","type":"education","lineage":["https://openalex.org/I169495764"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Anna Okopi\u0144ska","raw_affiliation_strings":["Institute of Physics, Jan Kochanowski University, \u015awie\u00b8tokrzyska 15, 25-406 Kielce, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Physics, Jan Kochanowski University, \u015awie\u00b8tokrzyska 15, 25-406 Kielce, Poland","institution_ids":["https://openalex.org/I169495764"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5030579100"],"corresponding_institution_ids":["https://openalex.org/I169495764"],"apc_list":{"value":3325,"currency":"USD","value_usd":3325},"apc_paid":null,"fwci":0.3086,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.40799753,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":87,"max":96},"biblio":{"volume":"46","issue":"8","first_page":"085303","last_page":"085303"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9077000021934509,"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":0.9077000021934509,"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/T10523","display_name":"Atomic and Molecular Physics","score":0.029100000858306885,"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/T11262","display_name":"Quantum Mechanics and Non-Hermitian Physics","score":0.02019999921321869,"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/resonance","display_name":"resonance","score":0.7929999828338623},{"id":"https://openalex.org/keywords/resonant-states","display_name":"resonant states","score":0.6140000224113464},{"id":"https://openalex.org/keywords/schrodinger-equation","display_name":"Schr\u00f6dinger equation","score":0.7910000085830688},{"id":"https://openalex.org/keywords/one-dimensional-potentials","display_name":"one-dimensional potentials","score":0.8159999847412109},{"id":"https://openalex.org/keywords/spherically-symmetric-potentials","display_name":"spherically symmetric potentials","score":0.9660000205039978},{"id":"https://openalex.org/keywords/bound-states","display_name":"bound states","score":0.4359999895095825}],"concepts":[{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.7311000227928162},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.6973999738693237},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5584999918937683},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.541100025177002},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5246999859809875},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5175999999046326},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5040000081062317},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5016999840736389},{"id":"https://openalex.org/C139210041","wikidata":"https://www.wikidata.org/wiki/Q2145840","display_name":"Resonance (particle physics)","level":2,"score":0.4880000054836273},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.48739999532699585},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.44859999418258667},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43560001254081726},{"id":"https://openalex.org/C23463724","wikidata":"https://www.wikidata.org/wiki/Q2308831","display_name":"Spectral method","level":2,"score":0.420199990272522},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.41260001063346863},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4018999934196472},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.382999986410141},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.38190001249313354},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.3382999897003174},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.32829999923706055},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28540000319480896},{"id":"https://openalex.org/C2983668108","wikidata":"https://www.wikidata.org/wiki/Q280453","display_name":"Spectral analysis","level":3,"score":0.2799000144004822},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.2702000141143799},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.2676999866962433},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.2662000060081482},{"id":"https://openalex.org/C2988995629","wikidata":"https://www.wikidata.org/wiki/Q2915729","display_name":"Matrix algebra","level":3,"score":0.2583000063896179},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.25369998812675476}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1088/1751-8113/46/8/085303","doi":"https://doi.org/10.1088/1751-8113/46/8/085303","is_oa":true,"landing_page_url":"https://doi.org/10.1088/1751-8113/46/8/085303","pdf_url":"https://iopscience.iop.org/article/10.1088/1751-8113/46/8/085303/pdf","source":{"id":"https://openalex.org/S79244937","display_name":"Journal of Physics A Mathematical and Theoretical","issn_l":"1751-8113","issn":["1751-8113","1751-8121"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-2","norway-1","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310311669","host_organization_name":"Institute of Physics","host_organization_lineage":["https://openalex.org/P4310311669"],"host_organization_lineage_names":["Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Physics A: Mathematical and Theoretical","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1211.2424","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1211.2424","pdf_url":"https://arxiv.org/pdf/1211.2424","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.1211.2424","doi":"https://doi.org/10.48550/arxiv.1211.2424","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1211.2424","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":"doi:10.1088/1751-8113/46/8/085303","doi":"https://doi.org/10.1088/1751-8113/46/8/085303","is_oa":true,"landing_page_url":"https://doi.org/10.1088/1751-8113/46/8/085303","pdf_url":"https://iopscience.iop.org/article/10.1088/1751-8113/46/8/085303/pdf","source":{"id":"https://openalex.org/S79244937","display_name":"Journal of Physics A Mathematical and Theoretical","issn_l":"1751-8113","issn":["1751-8113","1751-8121"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-2","norway-1","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310311669","host_organization_name":"Institute of Physics","host_organization_lineage":["https://openalex.org/P4310311669"],"host_organization_lineage_names":["Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Physics A: Mathematical and Theoretical","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320338080","display_name":"European Social Fund","ror":"https://ror.org/00k4n6c32"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1985994523.pdf","grobid_xml":"https://content.openalex.org/works/W1985994523.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W1554405298","https://openalex.org/W1649271673","https://openalex.org/W1964261024","https://openalex.org/W1966385690","https://openalex.org/W1976767534","https://openalex.org/W1979293498","https://openalex.org/W1992125257","https://openalex.org/W1993997085","https://openalex.org/W2002351582","https://openalex.org/W2005376349","https://openalex.org/W2006733885","https://openalex.org/W2010561889","https://openalex.org/W2015825250","https://openalex.org/W2018044998","https://openalex.org/W2021556327","https://openalex.org/W2028558199","https://openalex.org/W2061277718","https://openalex.org/W2062075513","https://openalex.org/W2066155200","https://openalex.org/W2092650388","https://openalex.org/W2117307511","https://openalex.org/W2123125496","https://openalex.org/W2149328975","https://openalex.org/W2158631147","https://openalex.org/W2173633196","https://openalex.org/W2231349387","https://openalex.org/W3121859240"],"related_works":["https://openalex.org/W2018044998","https://openalex.org/W1986094561","https://openalex.org/W2015825250","https://openalex.org/W2085200073","https://openalex.org/W2487691494","https://openalex.org/W7095183286","https://openalex.org/W2015021213","https://openalex.org/W1972224694","https://openalex.org/W2013481039","https://openalex.org/W2037194983"],"abstract_inverted_index":{"The":[0,54,133,148],"Rayleigh\u2013Ritz":[1,49,104],"procedure":[2],"for":[3,113,126],"determining":[4],"bound":[5],"states":[6,34,125],"of":[7,15,22,29,46,59,68,78,116,122],"the":[8,16,23,30,39,44,47,60,66,76,79,89,102,114,118,123],"Schr\u00f6dinger":[9],"equation":[10],"relies":[11],"on":[12],"spectral":[13],"representation":[14],"solution":[17],"as":[18,73],"a":[19,57],"linear":[20],"combination":[21],"basis":[24,58,97],"functions.":[25],"Several":[26],"possible":[27],"extensions":[28],"method":[31,50,55,134],"to":[32,51,74,84,91,153],"resonance":[33],"have":[35],"been":[36],"considered":[37],"in":[38],"literature.":[40],"Here":[41],"we":[42,99],"propose":[43],"application":[45],"optimized":[48,103],"this":[52],"end.":[53],"uses":[56],"functions":[61],"containing":[62],"adjustable":[63],"nonlinear":[64],"parameters,":[65],"values":[67],"which":[69],"are":[70],"fixed":[71],"so":[72],"make":[75],"trace":[77],"variational":[80],"matrix":[81],"stationary.":[82],"Generalization":[83],"resonances":[85],"proceeds":[86],"by":[87],"allowing":[88],"parameters":[90,108],"be":[92],"complex":[93,107],"numbers.":[94],"Using":[95],"various":[96,127],"sets,":[98],"demonstrate":[100],"that":[101],"scheme":[105],"with":[106],"provides":[109],"an":[110],"effective":[111],"algorithm":[112],"determination":[115],"both":[117],"energy":[119],"and":[120,129],"lifetime":[121],"resonant":[124],"one-dimensional":[128],"spherically":[130],"symmetric":[131],"potentials.":[132],"is":[135],"computationally":[136],"inexpensive":[137],"since":[138],"it":[139],"does":[140],"not":[141],"require":[142],"iterations":[143],"or":[144],"predetermined":[145],"initial":[146],"values.":[147],"convergence":[149],"rate":[150],"compares":[151],"favorably":[152],"other":[154],"approaches.":[155]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2016-06-24T00:00:00"}