{"id":"https://openalex.org/W2075114155","doi":"https://doi.org/10.1137/13091436x","title":"Dimension Reduction of the Schr\u00f6dinger Equation with Coulomb and Anisotropic Confining Potentials","display_name":"Dimension Reduction of the Schr\u00f6dinger Equation with Coulomb and Anisotropic Confining Potentials","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2075114155","doi":"https://doi.org/10.1137/13091436x","mag":"2075114155"},"language":"en","primary_location":{"id":"doi:10.1137/13091436x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/13091436x","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Applied 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/A5100759028","display_name":"Weizhu Bao","orcid":"https://orcid.org/0000-0003-3418-9625"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Weizhu Bao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021661768","display_name":"Huaiyu Jian","orcid":"https://orcid.org/0000-0001-7238-1939"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Huaiyu Jian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010896631","display_name":"Norbert J. Mauser","orcid":"https://orcid.org/0000-0001-9262-8943"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Norbert J. Mauser","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5100419892","display_name":"Yong Zhang","orcid":"https://orcid.org/0000-0003-4768-4780"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yong Zhang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.2105,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.87755417,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"73","issue":"6","first_page":"2100","last_page":"2123"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11965","display_name":"Quantum, superfluid, helium dynamics","score":0.9984999895095825,"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/T11965","display_name":"Quantum, superfluid, helium dynamics","score":0.9984999895095825,"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/T10425","display_name":"Cold Atom Physics and Bose-Einstein Condensates","score":0.9972000122070312,"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/T10382","display_name":"Quantum and electron transport phenomena","score":0.9969000220298767,"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/laplace-operator","display_name":"Laplace operator","score":0.6634321808815002},{"id":"https://openalex.org/keywords/adiabatic-process","display_name":"Adiabatic process","score":0.6606863141059875},{"id":"https://openalex.org/keywords/poissons-equation","display_name":"Poisson's equation","score":0.5723780393600464},{"id":"https://openalex.org/keywords/schr\u00f6dinger-equation","display_name":"Schr\u00f6dinger equation","score":0.5426090955734253},{"id":"https://openalex.org/keywords/dimensional-reduction","display_name":"Dimensional reduction","score":0.531123161315918},{"id":"https://openalex.org/keywords/coulomb","display_name":"Coulomb","score":0.5240780711174011},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.49399858713150024},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.48337501287460327},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.46246761083602905},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.44170618057250977},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4324834942817688},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.42095616459846497},{"id":"https://openalex.org/keywords/ground-state","display_name":"Ground state","score":0.417430579662323},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3665439188480377},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.29815322160720825},{"id":"https://openalex.org/keywords/electron","display_name":"Electron","score":0.21107646822929382},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.19472137093544006}],"concepts":[{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.6634321808815002},{"id":"https://openalex.org/C109663097","wikidata":"https://www.wikidata.org/wiki/Q182453","display_name":"Adiabatic process","level":2,"score":0.6606863141059875},{"id":"https://openalex.org/C96716743","wikidata":"https://www.wikidata.org/wiki/Q827688","display_name":"Poisson's equation","level":2,"score":0.5723780393600464},{"id":"https://openalex.org/C63036615","wikidata":"https://www.wikidata.org/wiki/Q165498","display_name":"Schr\u00f6dinger equation","level":2,"score":0.5426090955734253},{"id":"https://openalex.org/C2780091087","wikidata":"https://www.wikidata.org/wiki/Q3092131","display_name":"Dimensional reduction","level":2,"score":0.531123161315918},{"id":"https://openalex.org/C9342510","wikidata":"https://www.wikidata.org/wiki/Q25406","display_name":"Coulomb","level":3,"score":0.5240780711174011},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.49399858713150024},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.48337501287460327},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.46246761083602905},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.44170618057250977},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4324834942817688},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.42095616459846497},{"id":"https://openalex.org/C69523127","wikidata":"https://www.wikidata.org/wiki/Q4480008","display_name":"Ground state","level":2,"score":0.417430579662323},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3665439188480377},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.29815322160720825},{"id":"https://openalex.org/C147120987","wikidata":"https://www.wikidata.org/wiki/Q2225","display_name":"Electron","level":2,"score":0.21107646822929382},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.19472137093544006},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/13091436x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/13091436x","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:scholarbank.nus.edu.sg:10635/103134","is_oa":false,"landing_page_url":"http://scholarbank.nus.edu.sg/handle/10635/103134","pdf_url":null,"source":{"id":"https://openalex.org/S7407052290","display_name":"National University of Singapore","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Scopus","raw_type":"Article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.395.6364","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.395.6364","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.nus.edu.sg/~bao/PS/dim-SP.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":52,"referenced_works":["https://openalex.org/W636566490","https://openalex.org/W1490801527","https://openalex.org/W1528287451","https://openalex.org/W1644925518","https://openalex.org/W1969372542","https://openalex.org/W1972307217","https://openalex.org/W1977857702","https://openalex.org/W1985640971","https://openalex.org/W1991602497","https://openalex.org/W2003541845","https://openalex.org/W2007233074","https://openalex.org/W2008100982","https://openalex.org/W2008824117","https://openalex.org/W2011066618","https://openalex.org/W2013529907","https://openalex.org/W2015685032","https://openalex.org/W2020469535","https://openalex.org/W2023646351","https://openalex.org/W2024709257","https://openalex.org/W2029106707","https://openalex.org/W2031375452","https://openalex.org/W2043365391","https://openalex.org/W2044662130","https://openalex.org/W2046913111","https://openalex.org/W2049161806","https://openalex.org/W2050338742","https://openalex.org/W2063683447","https://openalex.org/W2065365545","https://openalex.org/W2068059131","https://openalex.org/W2069970911","https://openalex.org/W2071438440","https://openalex.org/W2075168679","https://openalex.org/W2078499533","https://openalex.org/W2083268850","https://openalex.org/W2083561837","https://openalex.org/W2088560338","https://openalex.org/W2091711176","https://openalex.org/W2116323997","https://openalex.org/W2121260562","https://openalex.org/W2144922956","https://openalex.org/W2158845426","https://openalex.org/W2163257413","https://openalex.org/W2169635804","https://openalex.org/W2270176086","https://openalex.org/W2315149965","https://openalex.org/W2562972486","https://openalex.org/W2963184103","https://openalex.org/W2971508903","https://openalex.org/W3094616800","https://openalex.org/W3101835573","https://openalex.org/W3148029235","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W3156661037","https://openalex.org/W2222996607","https://openalex.org/W2021443407","https://openalex.org/W2547767329","https://openalex.org/W2728265500","https://openalex.org/W2057705701","https://openalex.org/W2154223327","https://openalex.org/W1923653460","https://openalex.org/W1528600615","https://openalex.org/W2026022070"],"abstract_inverted_index":{"Abstract.":[0],"We":[1],"consider":[2],"dimension":[3,63,113,138],"reduction":[4,114,139],"for":[5,70,92,111,136,189],"the":[6,13,26,41,56,77,94,112,137,141,150,183,191,198,208,219],"three":[7],"dimensional":[8,23,99],"(3D)":[9],"Sch\u00f6dinger":[10],"equation":[11],"with":[12],"Coulomb":[14,192],"interaction":[15,193],"and":[16,38,55,66,74,80,88,108,119,128,147,216,221,225],"an":[17],"anisotropic":[18],"confining":[19],"potential":[20,96],"to":[21,104,117,121,159,186],"lower":[22,98],"models":[24,82],"in":[25,32,51,61,97,123,140,154,194,196,223,227],"limit":[27],"of":[28,76,125,166,201,207,218],"infinitely":[29],"strong":[30],"confinement":[31],"two":[33,52],"or":[34,46],"one":[35,62],"space":[36],"dimensions":[37,53],"obtain":[39],"formally":[40],"surface":[42,47],"adiabatic":[43,58],"model":[44,49,59,185],"(SAM)":[45],"density":[48],"(SDM)":[50],"(2D)":[54],"line":[57],"(LAM)":[60],"(1D).":[64],"Efficient":[65],"accurate":[67,89],"numerical":[68,90],"methods":[69],"computing":[71],"ground":[72,126,214],"states":[73,215],"dynamics":[75,217],"SAM,":[78],"SDM":[79,180,222],"LAM":[81,226],"are":[83,102],"presented":[84],"based":[85],"on":[86],"efficient":[87],"schemes":[91],"evaluating":[93],"effective":[95],"models.":[100],"They":[101],"applied":[103],"find":[105],"numerically":[106],"convergence":[107,109],"rates":[110],"from":[115],"3D":[116,120],"2D":[118,155,177,195,224],"1D":[122,228],"terms":[124],"state":[127],"dynamics,":[129],"which":[130,197],"confirm":[131],"some":[132],"existing":[133],"analytical":[134],"results":[135],"literatures.":[142],"In":[143],"particular,":[144],"we":[145,212],"explain":[146],"demonstrate":[148],"that":[149],"standard":[151],"Schr\u00f6dinger-Poisson":[152],"system":[153],"is":[156,204],"not":[157],"appropriate":[158],"simulate":[160],"a":[161,171,176],"\u201c2D":[162],"electron":[163],"gas":[164],"\u201d":[165],"point":[167],"particles":[168],"confined":[169],"into":[170],"plane":[172],"(or":[173],"more":[174],"general":[175],"manifold),":[178],"whereas":[179],"should":[181],"be":[182,187],"correct":[184],"used":[188,205],"describing":[190],"square":[199],"root":[200],"Laplacian":[202,209],"operator":[203],"instead":[206],"operator.":[210],"Finally,":[211],"report":[213],"SAM":[220],"under":[229],"different":[230],"setups.":[231]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
