{"id":"https://openalex.org/W1985198358","doi":"https://doi.org/10.1063/1.1670738","title":"Calculation of Matrix Elements for One-Dimensional Quantum-Mechanical Problems","display_name":"Calculation of Matrix Elements for One-Dimensional Quantum-Mechanical Problems","publication_year":1968,"publication_date":"1968-11-01","ids":{"openalex":"https://openalex.org/W1985198358","doi":"https://doi.org/10.1063/1.1670738","mag":"1985198358"},"language":"en","primary_location":{"id":"doi:10.1063/1.1670738","doi":"https://doi.org/10.1063/1.1670738","is_oa":false,"landing_page_url":"https://doi.org/10.1063/1.1670738","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"},"parent_works":[],"lineage":["https://openalex.org/W1985198358"],"child_works_count":0,"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/A5112186446","display_name":"A S Dickinson","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"A. S. Dickinson","raw_affiliation_strings":["University of Wisconsin Theoretical Chemistry Institute, Madison, Wisconsin 53706"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Wisconsin Theoretical Chemistry Institute, Madison, Wisconsin 53706","institution_ids":["https://openalex.org/I135310074"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047492629","display_name":"Phillip R. Certain","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"P. R. Certain","raw_affiliation_strings":["University of Wisconsin Theoretical Chemistry Institute, Madison, Wisconsin 53706"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Wisconsin Theoretical Chemistry Institute, Madison, Wisconsin 53706","institution_ids":["https://openalex.org/I135310074"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I135310074"],"apc_list":{"value":3500,"currency":"USD","value_usd":3500},"apc_paid":null,"fwci":1.1487,"has_fulltext":false,"cited_by_count":445,"citation_normalized_percentile":{"value":0.71780822,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":100},"biblio":{"volume":"49","issue":"9","first_page":"4209","last_page":"4211"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9023000001907349,"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"}},"topics":[{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9023000001907349,"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"}},{"id":"https://openalex.org/T11416","display_name":"Numerical Solvers for Ordinary Differential Equations","score":0.04349999874830246,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.01720000058412552,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/matrix-elements","display_name":"matrix elements","score":0.9779999852180481},{"id":"https://openalex.org/keywords/transformation-theory","display_name":"transformation theory","score":0.7559999823570251},{"id":"https://openalex.org/keywords/gaussian-quadrature","display_name":"Gaussian quadrature","score":0.9399999976158142},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"orthogonal polynomials","score":0.968999981880188}],"concepts":[{"id":"https://openalex.org/C5806529","wikidata":"https://www.wikidata.org/wiki/Q2365325","display_name":"Orthonormal basis","level":2,"score":0.8310139775276184},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.7537639737129211},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.6624146103858948},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.5768353343009949},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5732128024101257},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.5731885433197021},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.541650116443634},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4516517221927643},{"id":"https://openalex.org/C54940322","wikidata":"https://www.wikidata.org/wiki/Q3997740","display_name":"Orthogonal transformation","level":2,"score":0.43568602204322815},{"id":"https://openalex.org/C165443888","wikidata":"https://www.wikidata.org/wiki/Q1482183","display_name":"Transformation matrix","level":3,"score":0.4132132828235626},{"id":"https://openalex.org/C92951342","wikidata":"https://www.wikidata.org/wiki/Q1411166","display_name":"Orthonormality","level":3,"score":0.41247236728668213},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3933791220188141},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36034199595451355},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3545105457305908},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3356495499610901},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.18569988012313843},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15751108527183533},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14385554194450378},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.13468226790428162},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C39920418","wikidata":"https://www.wikidata.org/wiki/Q11476","display_name":"Kinematics","level":2,"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1063/1.1670738","doi":"https://doi.org/10.1063/1.1670738","is_oa":false,"landing_page_url":"https://doi.org/10.1063/1.1670738","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":10,"referenced_works":["https://openalex.org/W611047215","https://openalex.org/W1992535195","https://openalex.org/W2006646579","https://openalex.org/W2014114127","https://openalex.org/W2023514390","https://openalex.org/W2035155528","https://openalex.org/W2094706090","https://openalex.org/W2120062331","https://openalex.org/W3003197133","https://openalex.org/W3038165843"],"related_works":["https://openalex.org/W2069910839","https://openalex.org/W2079271830","https://openalex.org/W2094706090","https://openalex.org/W1970283165","https://openalex.org/W2098631193","https://openalex.org/W2081572824","https://openalex.org/W2032580149","https://openalex.org/W2154963393","https://openalex.org/W3000465021","https://openalex.org/W2043143784"],"abstract_inverted_index":{"A":[0],"simple":[1],"method":[2],"proposed":[3],"by":[4],"Harris":[5],"et":[6],"al.":[7],"using":[8],"the":[9,15,18,39],"techniques":[10],"of":[11,17,21,43],"transformation":[12],"theory":[13],"for":[14],"generation":[16],"matrix":[19],"elements":[20],"one-dimensional":[22],"potential":[23],"functions":[24],"in":[25],"a":[26],"discrete,":[27],"orthonormal":[28],"basis":[29,40,47],"is":[30,41,53],"shown":[31],"to":[32,35],"be":[33],"equivalent":[34],"Gaussian":[36],"quadratures":[37],"when":[38],"constructed":[42],"orthogonal":[44],"polynomials.":[45],"The":[46],"exp(in\u03b8)":[48],"on":[49],"(\u2212":[50],"\u03c0,":[51],"\u03c0)":[52],"also":[54],"discussed.":[55]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":11},{"year":2017,"cited_by_count":9},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":12},{"year":2014,"cited_by_count":10},{"year":2013,"cited_by_count":9},{"year":2012,"cited_by_count":16}],"updated_date":"2026-11-12T12:28:57.059296","created_date":"2016-06-24T00:00:00"}
