{"id":"https://openalex.org/W2000689010","doi":"https://doi.org/10.1119/perc.2013.pr.074","title":"Investigating Student Difficulties with Dirac Notation","display_name":"Investigating Student Difficulties with Dirac Notation","publication_year":2014,"publication_date":"2014-02-01","ids":{"openalex":"https://openalex.org/W2000689010","doi":"https://doi.org/10.1119/perc.2013.pr.074","mag":"2000689010"},"language":"en","primary_location":{"id":"doi:10.1119/perc.2013.pr.074","doi":"https://doi.org/10.1119/perc.2013.pr.074","is_oa":true,"landing_page_url":"https://doi.org/10.1119/perc.2013.pr.074","pdf_url":"https://www.per-central.org/items/perc/3696.pdf","source":{"id":"https://openalex.org/S4306498225","display_name":"Physics Education Research Conference (PERC)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physics Education Research Conference Proceedings","raw_type":"proceedings-article"},"volume":null,"type":"conference-paper","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.per-central.org/items/perc/3696.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Chandralekha Singh","orcid":"https://orcid.org/0000-0002-1234-5458","observed_orcids":["https://orcid.org/0000-0002-1234-5458"]},"institutions":[{"id":"https://openalex.org/I170201317","display_name":"University of Pittsburgh","ror":"https://ror.org/01an3r305","country_code":"US","type":"education","lineage":["https://openalex.org/I170201317"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Chandralekha Singh","raw_affiliation_strings":["Department of Physics and Astronomy , University of Pittsburgh , Pittsburgh , PA , 15260 , USA"],"raw_orcid":"https://orcid.org/0000-0002-1234-5458","affiliations":[{"raw_affiliation_string":"Department of Physics and Astronomy , University of Pittsburgh , Pittsburgh , PA , 15260 , USA","institution_ids":["https://openalex.org/I170201317"]}]},{"author_position":"last","author":{"id":null,"display_name":"Emily Marshman","orcid":"https://orcid.org/0000-0003-3962-5270","observed_orcids":["https://orcid.org/0000-0003-3962-5270"]},"institutions":[{"id":"https://openalex.org/I170201317","display_name":"University of Pittsburgh","ror":"https://ror.org/01an3r305","country_code":"US","type":"education","lineage":["https://openalex.org/I170201317"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Emily Marshman","raw_affiliation_strings":["Department of Physics and Astronomy , University of Pittsburgh , Pittsburgh , PA , 15260 , USA"],"raw_orcid":"https://orcid.org/0000-0003-3962-5270","affiliations":[{"raw_affiliation_string":"Department of Physics and Astronomy , University of Pittsburgh , Pittsburgh , PA , 15260 , USA","institution_ids":["https://openalex.org/I170201317"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I170201317"],"apc_list":null,"apc_paid":null,"fwci":9.0381,"has_fulltext":true,"cited_by_count":21,"citation_normalized_percentile":{"value":0.96823754,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"345","last_page":"348"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10072","display_name":"Science Education and Pedagogy","score":0.8916000127792358,"subfield":{"id":"https://openalex.org/subfields/3304","display_name":"Education"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10072","display_name":"Science Education and Pedagogy","score":0.8916000127792358,"subfield":{"id":"https://openalex.org/subfields/3304","display_name":"Education"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12931","display_name":"Educational Methods and Outcomes","score":0.03139999881386757,"subfield":{"id":"https://openalex.org/subfields/3304","display_name":"Education"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11875","display_name":"Statistics Education and Methodologies","score":0.013100000098347664,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/dirac-notation","display_name":"Dirac notation","score":0.9980000257492065},{"id":"https://openalex.org/keywords/bra-ket-notation","display_name":"bra-ket notation","score":0.8999999761581421},{"id":"https://openalex.org/keywords/quantum-mechanics-education","display_name":"quantum mechanics education","score":0.8169999718666077},{"id":"https://openalex.org/keywords/student-misconceptions","display_name":"student misconceptions","score":0.8090000152587891},{"id":"https://openalex.org/keywords/think-aloud","display_name":"think-aloud","score":0.8230000138282776},{"id":"https://openalex.org/keywords/student-reasoning","display_name":"student reasoning","score":0.31299999356269836}],"concepts":[{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.9290000200271606},{"id":"https://openalex.org/C61039578","wikidata":"https://www.wikidata.org/wiki/Q604279","display_name":"Dirac (video compression format)","level":3,"score":0.6478000283241272},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.6359000205993652},{"id":"https://openalex.org/C3020528894","wikidata":"https://www.wikidata.org/wiki/Q20820271","display_name":"Graduate students","level":2,"score":0.5166000127792358},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4487000107765198},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.4171000123023987},{"id":"https://openalex.org/C2780385302","wikidata":"https://www.wikidata.org/wiki/Q367158","display_name":"Protocol (science)","level":3,"score":0.32829999923706055},{"id":"https://openalex.org/C2775945657","wikidata":"https://www.wikidata.org/wiki/Q381442","display_name":"Structuring","level":2,"score":0.31850001215934753},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.296099990606308},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.29319998621940613},{"id":"https://openalex.org/C24457124","wikidata":"https://www.wikidata.org/wiki/Q1140046","display_name":"Mathematical notation","level":3,"score":0.2734000086784363},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.257099986076355}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1119/perc.2013.pr.074","doi":"https://doi.org/10.1119/perc.2013.pr.074","is_oa":true,"landing_page_url":"https://doi.org/10.1119/perc.2013.pr.074","pdf_url":"https://www.per-central.org/items/perc/3696.pdf","source":{"id":"https://openalex.org/S4306498225","display_name":"Physics Education Research Conference (PERC)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physics Education Research Conference Proceedings","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1510.01296","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1510.01296","pdf_url":"https://arxiv.org/pdf/1510.01296","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:compadre.org:13149","doi":null,"is_oa":true,"landing_page_url":"https://www.compadre.org/Repository/document/ServeFile.cfm?ID=13149&DocID=3696","pdf_url":null,"source":{"id":"https://openalex.org/S4306400571","display_name":"The Physics Video Demonstration Database (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Reference Material"},{"id":"doi:10.48550/arxiv.1510.01296","doi":"https://doi.org/10.48550/arxiv.1510.01296","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1510.01296","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.1119/perc.2013.pr.074","doi":"https://doi.org/10.1119/perc.2013.pr.074","is_oa":true,"landing_page_url":"https://doi.org/10.1119/perc.2013.pr.074","pdf_url":"https://www.per-central.org/items/perc/3696.pdf","source":{"id":"https://openalex.org/S4306498225","display_name":"Physics Education Research Conference (PERC)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physics Education Research Conference Proceedings","raw_type":"proceedings-article"},"sustainable_development_goals":[{"score":0.8278999924659729,"id":"https://metadata.un.org/sdg/4","display_name":"Quality education"}],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1827504030","display_name":"Development of Research-Based Tools for Teaching Quantum Mechanics","funder_award_id":"1202909","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6630461414","display_name":"Peer Instruction for Quantum Mechanics","funder_award_id":"0968891","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2000689010.pdf","grobid_xml":"https://content.openalex.org/works/W2000689010.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Quantum":[0],"mechanics":[1],"is":[2,12,105],"challenging":[3],"even":[4],"for":[5],"advanced":[6,28],"undergraduate":[7,29],"and":[8,30,41,46,78],"graduate":[9,31],"students.Dirac":[10],"notation":[11,15,77,86,101],"a":[13,56,61,91],"convenient":[14],"used":[16],"extensively":[17],"in":[18,83,90],"quantum":[19],"mechanics.We":[20],"have":[21,33],"been":[22],"investigating":[23],"the":[24,27,65],"difficulties":[25],"that":[26,71],"students":[32,45,54,73],"with":[34,52,75],"Dirac":[35,76,100],"notation.We":[36],"administered":[37],"written":[38],"free":[39],"response":[40],"multiple-choice":[42],"questions":[43,89,98],"to":[44,59],"also":[47],"conducted":[48],"semi-structured":[49],"individual":[50],"interviews":[51],"23":[53],"using":[55,84],"think-aloud":[57],"protocol":[58],"obtain":[60],"better":[62],"understanding":[63],"of":[64],"rationale":[66],"behind":[67],"their":[68],"responses.We":[69],"find":[70],"many":[72],"struggle":[74],"they":[79,96],"are":[80],"not":[81,104],"consistent":[82],"this":[85],"across":[87],"various":[88],"given":[92],"test.In":[93],"particular,":[94],"whether":[95],"answer":[97],"involving":[99],"correctly":[102],"or":[103],"context":[106],"dependent.":[107]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":4}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2016-06-24T00:00:00"}