{"id":"https://openalex.org/W1584961784","doi":null,"title":"Time-dependent variational principle for quantum dynamics in the Schrodinger-picture","display_name":"Time-dependent variational principle for quantum dynamics in the Schrodinger-picture","publication_year":1986,"publication_date":"1986-01-01","ids":{"openalex":"https://openalex.org/W1584961784","mag":"1584961784"},"language":"en","primary_location":{"id":"pmh:info:ark/67531/metadc1086497","doi":null,"is_oa":true,"landing_page_url":"https://digital.library.unt.edu/ark:/67531/metadc1086497/","pdf_url":"https://digital.library.unt.edu/ark:/67531/metadc1086497/","source":{"id":"https://openalex.org/S4306400792","display_name":"University of North Texas Digital Library (University of North Texas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I123534392","host_organization_name":"University of North Texas","host_organization_lineage":["https://openalex.org/I123534392"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"4. symposium on current trends in physics, Bhubaneswar, India, 24 Feb 1986","raw_type":"Article"},"volume":null,"type":"conference-paper","indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://digital.library.unt.edu/ark:/67531/metadc1086497/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011709906","display_name":"Fred Cooper","orcid":"https://orcid.org/0000-0002-2594-4169","observed_orcids":["https://orcid.org/0000-0002-2594-4169"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fred Cooper","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-2594-4169","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5112761867","display_name":"So-Young Pi","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"S.-Y. Pi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.05420561,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.492900013923645,"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.492900013923645,"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/T11416","display_name":"Numerical methods for differential equations","score":0.1860000044107437,"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/T11804","display_name":"Quantum many-body systems","score":0.1639000028371811,"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/time-dependent-variational-principle","display_name":"time-dependent variational principle","score":0.9919999837875366},{"id":"https://openalex.org/keywords/schrodinger-picture","display_name":"Schr\u00f6dinger picture","score":0.8610000014305115},{"id":"https://openalex.org/keywords/functional-schrodinger-equation","display_name":"functional Schr\u00f6dinger equation","score":0.9539999961853027},{"id":"https://openalex.org/keywords/quantum-field-theory","display_name":"quantum field theory","score":0.9490000009536743},{"id":"https://openalex.org/keywords/gaussian-wave-packets","display_name":"Gaussian wave packets","score":0.7630000114440918},{"id":"https://openalex.org/keywords/quantum-tunneling","display_name":"quantum tunneling","score":0.8820000290870667},{"id":"https://openalex.org/keywords/quantum-dynamics","display_name":"quantum dynamics","score":0.8410000205039978}],"concepts":[{"id":"https://openalex.org/C63036615","wikidata":"https://www.wikidata.org/wiki/Q165498","display_name":"Schr\u00f6dinger equation","level":2,"score":0.6894320249557495},{"id":"https://openalex.org/C194800363","wikidata":"https://www.wikidata.org/wiki/Q8588","display_name":"Schr\u00f6dinger's cat","level":2,"score":0.5866370797157288},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.5361679792404175},{"id":"https://openalex.org/C106978608","wikidata":"https://www.wikidata.org/wiki/Q1412691","display_name":"Wave packet","level":2,"score":0.5297951102256775},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5278035402297974},{"id":"https://openalex.org/C15184713","wikidata":"https://www.wikidata.org/wiki/Q7269042","display_name":"Quantum dynamics","level":3,"score":0.5111117959022522},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4987833499908447},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.4759092926979065},{"id":"https://openalex.org/C120398109","wikidata":"https://www.wikidata.org/wiki/Q175751","display_name":"Quantum tunnelling","level":2,"score":0.4739408791065216},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.4525931179523468},{"id":"https://openalex.org/C113603373","wikidata":"https://www.wikidata.org/wiki/Q2362761","display_name":"Wave function","level":2,"score":0.4469338357448578},{"id":"https://openalex.org/C9259290","wikidata":"https://www.wikidata.org/wiki/Q745215","display_name":"Variational principle","level":2,"score":0.43814817070961}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:info:ark/67531/metadc1086497","doi":null,"is_oa":true,"landing_page_url":"https://digital.library.unt.edu/ark:/67531/metadc1086497/","pdf_url":"https://digital.library.unt.edu/ark:/67531/metadc1086497/","source":{"id":"https://openalex.org/S4306400792","display_name":"University of North Texas Digital Library (University of North Texas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I123534392","host_organization_name":"University of North Texas","host_organization_lineage":["https://openalex.org/I123534392"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"4. symposium on current trends in physics, Bhubaneswar, India, 24 Feb 1986","raw_type":"Article"},{"id":"pmh:oai:osti.gov:5706744","doi":null,"is_oa":true,"landing_page_url":"https://www.osti.gov/biblio/5706744","pdf_url":"https://www.osti.gov/servlets/purl/5706744","source":{"id":"https://openalex.org/S4306402487","display_name":"OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I139351228","host_organization_name":"Office of Scientific and Technical Information","host_organization_lineage":["https://openalex.org/I139351228"],"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":null},{"id":"mag:1584961784","doi":null,"is_oa":true,"landing_page_url":"https://www.osti.gov/biblio/5706744","pdf_url":null,"source":{"id":"https://openalex.org/S4306402487","display_name":"OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I139351228","host_organization_name":"Office of Scientific and Technical Information","host_organization_lineage":["https://openalex.org/I139351228"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information)","raw_type":null}],"best_oa_location":{"id":"pmh:info:ark/67531/metadc1086497","doi":null,"is_oa":true,"landing_page_url":"https://digital.library.unt.edu/ark:/67531/metadc1086497/","pdf_url":"https://digital.library.unt.edu/ark:/67531/metadc1086497/","source":{"id":"https://openalex.org/S4306400792","display_name":"University of North Texas Digital Library (University of North Texas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I123534392","host_organization_name":"University of North Texas","host_organization_lineage":["https://openalex.org/I123534392"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"4. symposium on current trends in physics, Bhubaneswar, India, 24 Feb 1986","raw_type":"Article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1584961784.pdf","grobid_xml":"https://content.openalex.org/works/W1584961784.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W387991","https://openalex.org/W1986663793","https://openalex.org/W2089822599","https://openalex.org/W2916006837","https://openalex.org/W2768518356","https://openalex.org/W177109454","https://openalex.org/W2083224325","https://openalex.org/W1997779393","https://openalex.org/W2117307511","https://openalex.org/W7093330070"],"abstract_inverted_index":{"Starting":[0],"with":[1],"the":[2,14],"exact":[3,24],"variational":[4],"formulation":[5],"of":[6,47],"quantum":[7,10,48],"mechanics":[8],"(or":[9],"field":[11,43],"theory)":[12],"in":[13,50,65],"Schroedinger":[15,26],"picture,":[16],"and":[17,36,41],"using":[18,69],"Gaussian":[19,54],"trail":[20],"wave":[21,55],"functions,":[22],"an":[23,52,59],"functional":[25],"equation":[27],"is":[28,34,67,74],"obtained.":[29],"The":[30,45],"time-dependent":[31],"Hartree-Fock":[32],"approximation":[33],"obtained":[35],"extended":[37],"to":[38,42],"many":[39],"oscillators":[40],"theory.":[44],"problem":[46],"roll,":[49],"which":[51],"initial":[53],"packet":[56],"starting":[57],"at":[58],"unstable":[60],"classical":[61],"equilibrium":[62],"point":[63],"evolves":[64],"time,":[66],"treated":[68],"this":[70],"formalism.":[71],"Quantum":[72],"tunnelling":[73],"also":[75],"studied.":[76],"(LEW)":[77]},"counts_by_year":[],"updated_date":"2026-10-14T16:39:01.820549","created_date":"2016-06-24T00:00:00"}