{"id":"https://openalex.org/W3080922628","doi":"https://doi.org/10.1080/00207160.2020.1812586","title":"Fourier spectral method on sparse grids for computing ground state of many-particle fractional Schr\u00f6dinger equations","display_name":"Fourier spectral method on sparse grids for computing ground state of many-particle fractional Schr\u00f6dinger equations","publication_year":2020,"publication_date":"2020-08-20","ids":{"openalex":"https://openalex.org/W3080922628","doi":"https://doi.org/10.1080/00207160.2020.1812586","mag":"3080922628"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2020.1812586","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2020.1812586","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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/A5009026017","display_name":"Xueyang Li","orcid":"https://orcid.org/0000-0002-6395-320X"},"institutions":[{"id":"https://openalex.org/I4610292","display_name":"Xiangtan University","ror":"https://ror.org/00xsfaz62","country_code":"CN","type":"education","lineage":["https://openalex.org/I4610292"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xueyang Li","raw_affiliation_strings":["School of Mathematics and Computational Science, Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computational Science, Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan, People's Republic of China","institution_ids":["https://openalex.org/I4610292"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046464565","display_name":"Aiguo Xiao","orcid":"https://orcid.org/0000-0003-2075-5040"},"institutions":[{"id":"https://openalex.org/I4610292","display_name":"Xiangtan University","ror":"https://ror.org/00xsfaz62","country_code":"CN","type":"education","lineage":["https://openalex.org/I4610292"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Aiguo Xiao","raw_affiliation_strings":["School of Mathematics and Computational Science, Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computational Science, Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan, People's Republic of China","institution_ids":["https://openalex.org/I4610292"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5009026017"],"corresponding_institution_ids":["https://openalex.org/I4610292"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.07922815,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"98","issue":"6","first_page":"1218","last_page":"1232"},"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":0.9994999766349792,"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":0.9994999766349792,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T11416","display_name":"Numerical methods for differential equations","score":0.9979000091552734,"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":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7177678346633911},{"id":"https://openalex.org/keywords/schr\u00f6dinger-equation","display_name":"Schr\u00f6dinger equation","score":0.636447548866272},{"id":"https://openalex.org/keywords/sparse-grid","display_name":"Sparse grid","score":0.5342219471931458},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.5074159502983093},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.5019512176513672},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.4732010066509247},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.40980032086372375},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37918686866760254},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08072403073310852}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7177678346633911},{"id":"https://openalex.org/C63036615","wikidata":"https://www.wikidata.org/wiki/Q165498","display_name":"Schr\u00f6dinger equation","level":2,"score":0.636447548866272},{"id":"https://openalex.org/C156439662","wikidata":"https://www.wikidata.org/wiki/Q7573793","display_name":"Sparse grid","level":2,"score":0.5342219471931458},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.5074159502983093},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.5019512176513672},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.4732010066509247},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40980032086372375},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37918686866760254},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08072403073310852}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160.2020.1812586","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2020.1812586","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.4699999988079071}],"awards":[{"id":"https://openalex.org/G5791526758","display_name":null,"funder_award_id":"16C1541","funder_id":"https://openalex.org/F4320311213","funder_display_name":"Education Department of Hunan Province"},{"id":"https://openalex.org/G7502106191","display_name":null,"funder_award_id":"11601461,11671343","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8647190440","display_name":null,"funder_award_id":"2016JJ3115","funder_id":"https://openalex.org/F4320322843","funder_display_name":"Natural Science Foundation of\u00a0Hunan Province"}],"funders":[{"id":"https://openalex.org/F4320311213","display_name":"Education Department of Hunan Province","ror":"https://ror.org/05ckg3w11"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322843","display_name":"Natural Science Foundation of\u00a0Hunan Province","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W204604922","https://openalex.org/W1494602634","https://openalex.org/W1570210712","https://openalex.org/W1972610584","https://openalex.org/W2006165875","https://openalex.org/W2007665140","https://openalex.org/W2008456540","https://openalex.org/W2012708209","https://openalex.org/W2020266362","https://openalex.org/W2027762816","https://openalex.org/W2038068268","https://openalex.org/W2050338742","https://openalex.org/W2056316273","https://openalex.org/W2071438440","https://openalex.org/W2072536983","https://openalex.org/W2086031034","https://openalex.org/W2088217578","https://openalex.org/W2132119675","https://openalex.org/W2277337617","https://openalex.org/W2278928686","https://openalex.org/W2412363489","https://openalex.org/W2461570565","https://openalex.org/W2755519002","https://openalex.org/W2791739651","https://openalex.org/W2796153035","https://openalex.org/W2911377707","https://openalex.org/W2916979351","https://openalex.org/W2980095939","https://openalex.org/W3101835573","https://openalex.org/W4255975175"],"related_works":["https://openalex.org/W2389430631","https://openalex.org/W2237649730","https://openalex.org/W3139755018","https://openalex.org/W2159052351","https://openalex.org/W2549465884","https://openalex.org/W2082446734","https://openalex.org/W4313560640","https://openalex.org/W2226718045","https://openalex.org/W2390226322","https://openalex.org/W4295217538"],"abstract_inverted_index":{"In":[0,62],"this":[1],"paper,":[2],"we":[3,66],"consider":[4,67],"the":[5,10,15,19,36,39,47,51,59,63,75,83,89,97,106,111,115,120,124,134,143,151,156,164,169],"Fourier":[6],"spectral":[7],"method":[8,54,109,139,159,167],"on":[9],"sparse":[11,26,107,137,157],"grids":[12,27],"for":[13,28,38,119,142,150],"computing":[14],"ground":[16,60],"state":[17],"of":[18,41,50,70,136,171],"many-particle":[20,29],"fractional":[21,30,71,76,85,90,153],"Schr\u00f6dinger":[22,31,72,77,86,91,154],"equations.":[23],"The":[24],"appropriate":[25],"equations":[32],"are":[33],"given,":[34],"and":[35,82,123],"estimation":[37],"number":[40,170],"grid":[42,108,138,158,166],"points":[43],"is":[44,55,102,130,160,173],"obtained.":[45],"Then,":[46],"iterative":[48],"scheme":[49],"inverse":[52],"power":[53],"presented":[56],"to":[57,104,132],"compute":[58],"state.":[61],"numerical":[64],"experiments,":[65],"two":[68],"kinds":[69],"equations,":[73],"i.e.":[74],"equation":[78,92],"with":[79,93],"harmonic":[80,94],"potential":[81],"electronic":[84,152],"equation.":[87],"For":[88],"potential,":[95],"when":[96,128,168],"scaled":[98],"Planck":[99],"constant":[100],"\u210f":[101,129],"equal":[103,131],"1,":[105],"has":[110],"obvious":[112],"advantages":[113],"in":[114],"high-resolution":[116],"approximation":[117],"both":[118],"integer-order":[121],"problem":[122],"fractional-order":[125,144],"problem,":[126],"but":[127],"1/4,":[133],"advantage":[135],"exists":[140],"only":[141],"problem.":[145],"We":[146],"also":[147],"show":[148],"that":[149],"equation,":[155],"much":[161],"better":[162],"than":[163],"full":[165],"electrons":[172],"relatively":[174],"large.":[175]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-08-15T07:11:24.734988","created_date":"2025-10-10T00:00:00"}