{"id":"https://openalex.org/W7225832989","doi":"https://doi.org/10.1140/epja/s10050-026-01989-z","title":"Numerical solution of the time-independent-wave-packet form of the Lippmann\u2013Schwinger equation: Nystrom method vs Chebyshev expansion of the resolvent operator","display_name":"Numerical solution of the time-independent-wave-packet form of the Lippmann\u2013Schwinger equation: Nystrom method vs Chebyshev expansion of the resolvent operator","publication_year":2026,"publication_date":"2026-11-11","ids":{"openalex":"https://openalex.org/W7225832989","doi":"https://doi.org/10.1140/epja/s10050-026-01989-z"},"language":"en","primary_location":{"id":"doi:10.1140/epja/s10050-026-01989-z","doi":"https://doi.org/10.1140/epja/s10050-026-01989-z","is_oa":true,"landing_page_url":"https://doi.org/10.1140/epja/s10050-026-01989-z","pdf_url":null,"source":{"id":"https://openalex.org/S4210173186","display_name":"The European Physical Journal A","issn_l":"1434-6001","issn":["1434-6001","1434-601X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-2","norway-1","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The European Physical Journal A","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1140/epja/s10050-026-01989-z","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5049076203","display_name":"Zeki C. Kuruo\u011flu","orcid":"https://orcid.org/0000-0001-6345-3822","observed_orcids":["https://orcid.org/0000-0001-6345-3822"]},"institutions":[{"id":"https://openalex.org/I168864056","display_name":"Bilkent University","ror":"https://ror.org/02vh8a032","country_code":"TR","type":"education","lineage":["https://openalex.org/I168864056"]}],"countries":["TR"],"is_corresponding":true,"raw_author_name":"Zeki C. Kuruo\u011flu","raw_affiliation_strings":["Department of Chemistry, Bilkent University, Bilkent, 06800, Ankara, Turkey"],"raw_orcid":"https://orcid.org/0000-0001-6345-3822","affiliations":[{"raw_affiliation_string":"Department of Chemistry, Bilkent University, Bilkent, 06800, Ankara, Turkey","institution_ids":["https://openalex.org/I168864056"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5049076203"],"corresponding_institution_ids":["https://openalex.org/I168864056"],"apc_list":{"value":3990,"currency":"USD","value_usd":3990},"apc_paid":{"value":3990,"currency":"USD","value_usd":3990},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"62","issue":"11","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":0.8276000022888184,"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":0.8276000022888184,"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":0.044599998742341995,"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/T11416","display_name":"Numerical Solvers for Ordinary Differential Equations","score":0.031199999153614044,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[],"concepts":[{"id":"https://openalex.org/C196267783","wikidata":"https://www.wikidata.org/wiki/Q4392490","display_name":"Resolvent","level":2,"score":0.8547000288963318},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7610999941825867},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5152999758720398},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4787999987602234},{"id":"https://openalex.org/C129785596","wikidata":"https://www.wikidata.org/wiki/Q619511","display_name":"Chebyshev polynomials","level":2,"score":0.4496000111103058},{"id":"https://openalex.org/C21424316","wikidata":"https://www.wikidata.org/wiki/Q718621","display_name":"Chebyshev filter","level":2,"score":0.41359999775886536},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.385699987411499},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.37880000472068787},{"id":"https://openalex.org/C90559484","wikidata":"https://www.wikidata.org/wiki/Q778379","display_name":"Expression (computer science)","level":2,"score":0.3564000129699707},{"id":"https://openalex.org/C106978608","wikidata":"https://www.wikidata.org/wiki/Q1412691","display_name":"Wave packet","level":2,"score":0.35499998927116394},{"id":"https://openalex.org/C19579662","wikidata":"https://www.wikidata.org/wiki/Q461145","display_name":"Energy operator","level":3,"score":0.35040000081062317},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33640000224113464},{"id":"https://openalex.org/C58677928","wikidata":"https://www.wikidata.org/wiki/Q911268","display_name":"D'Alembert operator","level":2,"score":0.3276999890804291},{"id":"https://openalex.org/C142484921","wikidata":"https://www.wikidata.org/wiki/Q3890369","display_name":"Chebyshev equation","level":4,"score":0.3231000006198883},{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.3093000054359436},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3059000074863434},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.3000999987125397},{"id":"https://openalex.org/C178009071","wikidata":"https://www.wikidata.org/wiki/Q93344","display_name":"Trigonometric functions","level":2,"score":0.29030001163482666},{"id":"https://openalex.org/C196512905","wikidata":"https://www.wikidata.org/wiki/Q2457511","display_name":"Chebyshev iteration","level":3,"score":0.29030001163482666},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.2883000075817108},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.2867000102996826},{"id":"https://openalex.org/C201292218","wikidata":"https://www.wikidata.org/wiki/Q740970","display_name":"Recurrence relation","level":2,"score":0.27390000224113464},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.2721000015735626},{"id":"https://openalex.org/C157097347","wikidata":"https://www.wikidata.org/wiki/Q1908689","display_name":"Mathieu function","level":2,"score":0.26980000734329224},{"id":"https://openalex.org/C191486275","wikidata":"https://www.wikidata.org/wiki/Q210028","display_name":"Scattering","level":2,"score":0.26269999146461487}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1140/epja/s10050-026-01989-z","doi":"https://doi.org/10.1140/epja/s10050-026-01989-z","is_oa":true,"landing_page_url":"https://doi.org/10.1140/epja/s10050-026-01989-z","pdf_url":null,"source":{"id":"https://openalex.org/S4210173186","display_name":"The European Physical Journal A","issn_l":"1434-6001","issn":["1434-6001","1434-601X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-2","norway-1","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The European Physical Journal A","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1140/epja/s10050-026-01989-z","doi":"https://doi.org/10.1140/epja/s10050-026-01989-z","is_oa":true,"landing_page_url":"https://doi.org/10.1140/epja/s10050-026-01989-z","pdf_url":null,"source":{"id":"https://openalex.org/S4210173186","display_name":"The European Physical Journal A","issn_l":"1434-6001","issn":["1434-6001","1434-601X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-2","norway-1","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The European Physical Journal A","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W1556559448","https://openalex.org/W1967612791","https://openalex.org/W1969926416","https://openalex.org/W1976291817","https://openalex.org/W1976733960","https://openalex.org/W1979517311","https://openalex.org/W1989398397","https://openalex.org/W2028578037","https://openalex.org/W2029721186","https://openalex.org/W2037783202","https://openalex.org/W2041453761","https://openalex.org/W2051609301","https://openalex.org/W2057634172","https://openalex.org/W2076196834","https://openalex.org/W2079813986","https://openalex.org/W2083452734","https://openalex.org/W2091046435","https://openalex.org/W2093449600","https://openalex.org/W2094022882","https://openalex.org/W2145114089","https://openalex.org/W2341107217","https://openalex.org/W2481422693","https://openalex.org/W4230168603","https://openalex.org/W4414091440","https://openalex.org/W7160853792"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"This":[1,54],"paper":[2],"computationally":[3],"explores":[4],"some":[5],"lesser-known":[6],"results":[7,104],"from":[8],"the":[9,15,20,24,40,43,50,61,74,81,84,88,106,109,114,119,122,136,140,147,157,167,176],"quantum":[10],"scattering":[11],"theory":[12],"that":[13],"gives":[14],"S-matrix":[16,32,168],"in":[17,153],"terms":[18],"of":[19,26,42,63,83,87,101,108,113,135,146,156,162],"resolvent":[21,148],"operator":[22,149],"through":[23],"mediation":[25],"time-independent":[27],"wave":[28,76,97],"packets":[29],"(TIWP).":[30],"The":[31],"at":[33,49,68],"a":[34,69,172],"given":[35,38,70],"energy":[36,71],"is":[37,126],"by":[39,150],"ratio":[41,62,82],"interacting":[44,89],"and":[45,65,90,95,143],"free":[46,66,91],"TIWP\u2019s":[47],"evaluated":[48],"corresponding":[51],"on-shell":[52],"momentum.":[53],"expression":[55,79],"can":[56],"also":[57],"be":[58],"expressed":[59],"as":[60],"full":[64],"resolvents":[67,92],"acting":[72],"on":[73,171],"pre-collision":[75,96],"packet.":[77],"Another":[78],"involves":[80],"matrix":[85],"elements":[86],"between":[93],"post-":[94],"packets.":[98],"Computational":[99,160],"implementations":[100],"these":[102,163],"formal":[103],"involve":[105],"solution":[107,134],"so-called":[110],"TIWP":[111],"form":[112],"Lippmann\u2013Schwinger":[115],"equation":[116,125,138],"(TIWP-LS).":[117],"In":[118],"present":[120],"contribution,":[121],"partial-wave":[123],"TIWP-LS":[124,137],"solved":[127],"using":[128],"two":[129],"schemes:":[130],"(i)":[131],"Direct":[132],"numerical":[133],"via":[139],"quadrature":[141],"discretization,":[142],"(ii)":[144],"Construction":[145],"an":[151],"expansion":[152],"Chebyshev":[154],"polynomials":[155],"scaled":[158],"Hamiltonian.":[159],"performances":[161],"procedures":[164],"to":[165],"compute":[166],"are":[169],"tested":[170],"model":[173],"potential":[174],"for":[175],"p-wave":[177],"case.":[178]},"counts_by_year":[],"updated_date":"2026-11-12T12:28:57.059296","created_date":"2026-11-12T00:00:00"}
