{"id":"https://openalex.org/W1986219311","doi":"https://doi.org/10.1063/1.436072","title":"Explicit integration method for the time-dependent Schrodinger equation for collision problems","display_name":"Explicit integration method for the time-dependent Schrodinger equation for collision problems","publication_year":1978,"publication_date":"1978-03-15","ids":{"openalex":"https://openalex.org/W1986219311","doi":"https://doi.org/10.1063/1.436072","mag":"1986219311"},"language":"en","primary_location":{"id":"doi:10.1063/1.436072","doi":"https://doi.org/10.1063/1.436072","is_oa":false,"landing_page_url":"https://doi.org/10.1063/1.436072","pdf_url":null,"source":{"id":"https://openalex.org/S77047749","display_name":"The Journal of Chemical Physics","issn_l":"0021-9606","issn":["0021-9606","1089-7690","1520-9032"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-1","ki-jl-1","medline","norway-1","poland-100","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310320257","host_organization_name":"American Institute of Physics","host_organization_lineage":["https://openalex.org/P4310320257"],"host_organization_lineage_names":["American Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Journal of Chemical Physics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"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/A5007528164","display_name":"Attila A\u015fkar","orcid":"https://orcid.org/0000-0003-0444-4787","observed_orcids":["https://orcid.org/0000-0003-0444-4787"]},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"A. Askar","raw_affiliation_strings":["School of Engineering and Applied Science, Princeton University, Princeton, New Jersey 08540"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Engineering and Applied Science, Princeton University, Princeton, New Jersey 08540","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111370042","display_name":"A. \u015e. \u00c7akmak","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"A. S. Cakmak","raw_affiliation_strings":["School of Engineering and Applied Science, Princeton University, Princeton, New Jersey 08540"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Engineering and Applied Science, Princeton University, Princeton, New Jersey 08540","institution_ids":["https://openalex.org/I20089843"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I20089843"],"apc_list":{"value":3500,"currency":"USD","value_usd":3500},"apc_paid":null,"fwci":1.3513,"has_fulltext":false,"cited_by_count":272,"citation_normalized_percentile":{"value":0.76124567,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":"68","issue":"6","first_page":"2794","last_page":"2798"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical Solvers for Ordinary Differential Equations","score":0.9984999895095825,"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"}},"topics":[{"id":"https://openalex.org/T11416","display_name":"Numerical Solvers for Ordinary Differential Equations","score":0.9984999895095825,"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"}},{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12727","display_name":"Singular Perturbation, Asymptotics and Difference Schemes","score":9.999999747378752e-05,"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/time-dependent-schrodinger-equation","display_name":"time-dependent Schr\u00f6dinger equation","score":0.9259999990463257},{"id":"https://openalex.org/keywords/explicit-integration-methods","display_name":"explicit integration methods","score":0.8309999704360962},{"id":"https://openalex.org/keywords/collision-processes","display_name":"collisional processes","score":0.6909999847412109},{"id":"https://openalex.org/keywords/numerical-stability","display_name":"numerical stability","score":0.7239999771118164},{"id":"https://openalex.org/keywords/unitarity","display_name":"unitarity","score":0.8669999837875366},{"id":"https://openalex.org/keywords/matrix-inversion-avoidance","display_name":"matrix inversion avoidance","score":0.4399999976158142}],"concepts":[{"id":"https://openalex.org/C121704057","wikidata":"https://www.wikidata.org/wiki/Q352070","display_name":"Collision","level":2,"score":0.6418583393096924},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6185678243637085},{"id":"https://openalex.org/C130295795","wikidata":"https://www.wikidata.org/wiki/Q3550684","display_name":"Unitarity","level":2,"score":0.5395841002464294},{"id":"https://openalex.org/C1893757","wikidata":"https://www.wikidata.org/wiki/Q3653001","display_name":"Inversion (geology)","level":3,"score":0.5376846194267273},{"id":"https://openalex.org/C63036615","wikidata":"https://www.wikidata.org/wiki/Q165498","display_name":"Schr\u00f6dinger equation","level":2,"score":0.5348504781723022},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5185397267341614},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4865659773349762},{"id":"https://openalex.org/C113603373","wikidata":"https://www.wikidata.org/wiki/Q2362761","display_name":"Wave function","level":2,"score":0.4472103714942932},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.41356849670410156},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3293578028678894},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2953253984451294},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.19412359595298767},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15393072366714478},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.12117865681648254},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C109007969","wikidata":"https://www.wikidata.org/wiki/Q749565","display_name":"Structural basin","level":2,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1063/1.436072","doi":"https://doi.org/10.1063/1.436072","is_oa":false,"landing_page_url":"https://doi.org/10.1063/1.436072","pdf_url":null,"source":{"id":"https://openalex.org/S77047749","display_name":"The Journal of Chemical Physics","issn_l":"0021-9606","issn":["0021-9606","1089-7690","1520-9032"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-1","ki-jl-1","medline","norway-1","poland-100","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310320257","host_organization_name":"American Institute of Physics","host_organization_lineage":["https://openalex.org/P4310320257"],"host_organization_lineage_names":["American Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Journal of Chemical Physics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W1965933784","https://openalex.org/W2001591740","https://openalex.org/W2014032943","https://openalex.org/W2026790510","https://openalex.org/W2075639668"],"related_works":["https://openalex.org/W3207441473","https://openalex.org/W2056964933","https://openalex.org/W4210453529","https://openalex.org/W4402774291","https://openalex.org/W2149197981","https://openalex.org/W2035218231","https://openalex.org/W2064740958","https://openalex.org/W1966991416","https://openalex.org/W2018694615","https://openalex.org/W3096368221"],"abstract_inverted_index":{"To":[0],"date,":[1],"only":[2],"the":[3,15,37,42,45,50,77,94,100,104,116],"implicit":[4,38,101],"(Crank\u2013Nicholson)":[5],"integration":[6,13],"method":[7,39,51,70,73,102],"has":[8],"ben":[9],"used":[10],"for":[11,18,36,115],"numerical":[12],"of":[14,44,79,97],"Schrodinger":[16],"equation":[17],"collision":[19],"processes.":[20],"The":[21],"standard":[22],"explicit":[23,69],"methods":[24],"are":[25],"known":[26],"to":[27,41,60,87,93,108],"be":[28,88],"unstable":[29],"and":[30,64,84],"a":[31,72],"high":[32],"price":[33],"is":[34,52,82,85],"paid":[35],"due":[40,59],"inversion":[43],"large":[46,65],"matrices":[47],"involved.":[48],"Furthermore,":[49],"prohibitive":[53],"in":[54,90],"more":[55],"than":[56,113],"two":[57,109],"dimensions":[58,92],"restrictions":[61],"on":[62],"memory":[63],"computation":[66],"times.":[67],"An":[68],"(i.e.,":[71],"which":[74],"doesn\u2019t":[75],"require":[76],"solution":[78],"simultaneous":[80],"equations)":[81],"presented,":[83],"shown":[86],"stable":[89],"n":[91],"same":[95],"order":[96],"accuracy":[98,112],"as":[99],"with":[103],"unitarity":[105],"being":[106],"secured":[107],"orders":[110],"higher":[111],"that":[114],"wave":[117],"function.":[118]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":10},{"year":2017,"cited_by_count":9},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":9},{"year":2012,"cited_by_count":9}],"updated_date":"2026-11-12T12:28:57.059296","created_date":"2016-06-24T00:00:00"}
