{"id":"https://openalex.org/W2032181547","doi":"https://doi.org/10.1137/s0895479800371530","title":"Eigenvalue Problems for One-Dimensional Discrete Schr\u00f6dinger Operators with Symmetric Boundary Conditions","display_name":"Eigenvalue Problems for One-Dimensional Discrete Schr\u00f6dinger Operators with Symmetric Boundary Conditions","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W2032181547","doi":"https://doi.org/10.1137/s0895479800371530","mag":"2032181547"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479800371530","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479800371530","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","raw_type":"journal-article"},"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/A5041798346","display_name":"Jonq Juang","orcid":"https://orcid.org/0000-0001-9563-8143"},"institutions":[{"id":"https://openalex.org/I148366613","display_name":"National Yang Ming Chiao Tung University","ror":"https://ror.org/00se2k293","country_code":"TW","type":"education","lineage":["https://openalex.org/I148366613"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Jonq Juang","raw_affiliation_strings":["National Yang Ming Chiao Tung University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Yang Ming Chiao Tung University","institution_ids":["https://openalex.org/I148366613"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101337552","display_name":"Wen\u2010Wei Lin","orcid":null},"institutions":[{"id":"https://openalex.org/I148366613","display_name":"National Yang Ming Chiao Tung University","ror":"https://ror.org/00se2k293","country_code":"TW","type":"education","lineage":["https://openalex.org/I148366613"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Wen-Wei Lin","raw_affiliation_strings":["National Yang Ming Chiao Tung University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Yang Ming Chiao Tung University","institution_ids":["https://openalex.org/I148366613"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000174968","display_name":"Shih-Feng Shieh","orcid":null},"institutions":[{"id":"https://openalex.org/I530967","display_name":"Toronto Metropolitan University","ror":"https://ror.org/05g13zd79","country_code":"CA","type":"education","lineage":["https://openalex.org/I530967"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Shih-Feng Shieh","raw_affiliation_strings":["Department of Mathematics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics","institution_ids":["https://openalex.org/I530967"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4912,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.60399218,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"23","issue":"2","first_page":"524","last_page":"533"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9884999990463257,"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":0.9884999990463257,"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/T13234","display_name":"advanced mathematical theories","score":0.9736999869346619,"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/T12589","display_name":"Differential Equations and Boundary Problems","score":0.9559999704360962,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8088666200637817},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7158231735229492},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5858107805252075},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5244484543800354},{"id":"https://openalex.org/keywords/schr\u00f6dinger-equation","display_name":"Schr\u00f6dinger equation","score":0.5047539472579956},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.49188995361328125},{"id":"https://openalex.org/keywords/discrete-spectrum","display_name":"Discrete spectrum","score":0.4870772659778595},{"id":"https://openalex.org/keywords/schr\u00f6dingers-cat","display_name":"Schr\u00f6dinger's cat","score":0.45376741886138916},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.10935184359550476},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09860309958457947}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8088666200637817},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7158231735229492},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5858107805252075},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5244484543800354},{"id":"https://openalex.org/C63036615","wikidata":"https://www.wikidata.org/wiki/Q165498","display_name":"Schr\u00f6dinger equation","level":2,"score":0.5047539472579956},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.49188995361328125},{"id":"https://openalex.org/C13487092","wikidata":"https://www.wikidata.org/wiki/Q5282061","display_name":"Discrete spectrum","level":3,"score":0.4870772659778595},{"id":"https://openalex.org/C194800363","wikidata":"https://www.wikidata.org/wiki/Q8588","display_name":"Schr\u00f6dinger's cat","level":2,"score":0.45376741886138916},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.10935184359550476},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09860309958457947}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/s0895479800371530","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479800371530","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.517.6098","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.517.6098","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://jupiter.math.nctu.edu.tw/~wwlin/papers_new/2001JLSp.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.953.5147","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.953.5147","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://ir.nctu.edu.tw:443/bitstream/11536/29246/1/000172891000014.pdf","raw_type":"text"},{"id":"pmh:oai:oaktrust.library.tamu.edu:1969.1/185457","is_oa":false,"landing_page_url":"https://hdl.handle.net/1969.1/185457","pdf_url":null,"source":{"id":"https://openalex.org/S4306400291","display_name":"OakTrust (Texas A&M University Libraries)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I91045830","host_organization_name":"Texas A&M University","host_organization_lineage":["https://openalex.org/I91045830"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.7400000095367432}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W259156686","https://openalex.org/W1540935623","https://openalex.org/W1669696816","https://openalex.org/W1680579736","https://openalex.org/W2051186530","https://openalex.org/W2075822844","https://openalex.org/W2090945912","https://openalex.org/W2104982909","https://openalex.org/W2105433369","https://openalex.org/W2161766186","https://openalex.org/W2962769555"],"related_works":["https://openalex.org/W1983082926","https://openalex.org/W2952745759","https://openalex.org/W2046663981","https://openalex.org/W2235306894","https://openalex.org/W1633290709","https://openalex.org/W153724988","https://openalex.org/W2349865015","https://openalex.org/W2133054979","https://openalex.org/W3103415543","https://openalex.org/W2982247499"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"investigate":[4],"the":[5,19,26],"one-dimensional":[6],"discrete":[7],"Schr\u00f6dinger":[8],"equation":[9],"with":[10],"general,":[11],"symmetric":[12],"boundary":[13],"conditions.":[14],"Our":[15],"results":[16],"primarily":[17],"concern":[18],"number":[20],"of":[21],"energy":[22],"states":[23],"lying":[24],"in":[25],"wells.":[27]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
