{"id":"https://openalex.org/W2592318129","doi":"https://doi.org/10.1140/epjd/e2017-80134-6","title":"Conditional quasi-exact solvability of the quantum planar pendulum and of its anti-isospectral hyperbolic counterpart","display_name":"Conditional quasi-exact solvability of the quantum planar pendulum and of its anti-isospectral hyperbolic counterpart","publication_year":2017,"publication_date":"2017-06-01","ids":{"openalex":"https://openalex.org/W2592318129","doi":"https://doi.org/10.1140/epjd/e2017-80134-6","mag":"2592318129"},"language":"en","primary_location":{"id":"doi:10.1140/epjd/e2017-80134-6","doi":"https://doi.org/10.1140/epjd/e2017-80134-6","is_oa":true,"landing_page_url":"https://doi.org/10.1140/epjd/e2017-80134-6","pdf_url":"https://link.springer.com/content/pdf/10.1140%2Fepjd%2Fe2017-80134-6.pdf","source":{"id":"https://openalex.org/S174148793","display_name":"The European Physical Journal D","issn_l":"1434-6060","issn":["1434-6060","1434-6079"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-1","ki-jl-1","norway-1","poland-40","russia-white-list-3"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The European Physical Journal D","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1140%2Fepjd%2Fe2017-80134-6.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030704908","display_name":"Simon Becker","orcid":"https://orcid.org/0000-0002-6703-9511","observed_orcids":["https://orcid.org/0000-0002-6703-9511"]},"institutions":[{"id":"https://openalex.org/I75951250","display_name":"Freie Universit\u00e4t Berlin","ror":"https://ror.org/046ak2485","country_code":"DE","type":"education","lineage":["https://openalex.org/I75951250"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Simon Becker","raw_affiliation_strings":["Institute for Mathematics, Freie Universit\u00e4t Berlin, Arnimallee 6, 14195, Berlin, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Mathematics, Freie Universit\u00e4t Berlin, Arnimallee 6, 14195, Berlin, Germany","institution_ids":["https://openalex.org/I75951250"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043254433","display_name":"Marjan Mirahmadi","orcid":"https://orcid.org/0000-0003-4038-2608","observed_orcids":["https://orcid.org/0000-0003-4038-2608"]},"institutions":[{"id":"https://openalex.org/I75951250","display_name":"Freie Universit\u00e4t Berlin","ror":"https://ror.org/046ak2485","country_code":"DE","type":"education","lineage":["https://openalex.org/I75951250"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Marjan Mirahmadi","raw_affiliation_strings":["Institute for Mathematics, Freie Universit\u00e4t Berlin, Arnimallee 6, 14195, Berlin, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Mathematics, Freie Universit\u00e4t Berlin, Arnimallee 6, 14195, Berlin, Germany","institution_ids":["https://openalex.org/I75951250"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Burkhard Schmidt","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I75951250","display_name":"Freie Universit\u00e4t Berlin","ror":"https://ror.org/046ak2485","country_code":"DE","type":"education","lineage":["https://openalex.org/I75951250"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Burkhard Schmidt","raw_affiliation_strings":["Institute for Mathematics, Freie Universit\u00e4t Berlin, Arnimallee 6, 14195, Berlin, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Mathematics, Freie Universit\u00e4t Berlin, Arnimallee 6, 14195, Berlin, Germany","institution_ids":["https://openalex.org/I75951250"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Konrad Schatz","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I2800875726","display_name":"Fritz Haber Institute of the Max Planck Society","ror":"https://ror.org/03k9qs827","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I2800875726"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Konrad Schatz","raw_affiliation_strings":["Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4\u20136, 14195, Berlin, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4\u20136, 14195, Berlin, Germany","institution_ids":["https://openalex.org/I2800875726"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5069284839","display_name":"B\u0159etislav Friedrich","orcid":"https://orcid.org/0000-0002-1299-4239","observed_orcids":["https://orcid.org/0000-0002-1299-4239"]},"institutions":[{"id":"https://openalex.org/I2800875726","display_name":"Fritz Haber Institute of the Max Planck Society","ror":"https://ror.org/03k9qs827","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I2800875726"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Bretislav Friedrich","raw_affiliation_strings":["Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4\u20136, 14195, Berlin, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4\u20136, 14195, Berlin, Germany","institution_ids":["https://openalex.org/I2800875726"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5069284839"],"corresponding_institution_ids":["https://openalex.org/I2800875726","https://openalex.org/I75951250"],"apc_list":{"value":3790,"currency":"USD","value_usd":3790},"apc_paid":{"value":3790,"currency":"USD","value_usd":3790},"fwci":0.8121,"has_fulltext":true,"cited_by_count":11,"citation_normalized_percentile":{"value":0.60541035,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":97},"biblio":{"volume":"71","issue":"6","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.38530001044273376,"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"}},"topics":[{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.38530001044273376,"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"}},{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.2937000095844269,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"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/T11262","display_name":"Quantum Mechanics and Non-Hermitian Physics","score":0.21250000596046448,"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/planar-pendulum","display_name":"planar pendulum","score":0.8989999890327454},{"id":"https://openalex.org/keywords/symmetry-analysis","display_name":"symmetry analysis","score":0.6380000114440918},{"id":"https://openalex.org/keywords/tridiagonal-matrix","display_name":"tridiagonal matrices","score":0.7639999985694885},{"id":"https://openalex.org/keywords/topological-indices","display_name":"topological indices","score":0.9919999837875366},{"id":"https://openalex.org/keywords/avoided-crossings","display_name":"avoided crossings","score":0.7390000224113464},{"id":"https://openalex.org/keywords/analytical-solution","display_name":"analytical solution","score":0.5590000152587891},{"id":"https://openalex.org/keywords/doublet-states","display_name":"doublet states","score":0.41999998688697815}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7613000273704529},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6866999864578247},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.6200000047683716},{"id":"https://openalex.org/C51647924","wikidata":"https://www.wikidata.org/wiki/Q1755277","display_name":"Tridiagonal matrix","level":3,"score":0.5286999940872192},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.4724000096321106},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4099000096321106},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4036000072956085},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.39570000767707825},{"id":"https://openalex.org/C24872484","wikidata":"https://www.wikidata.org/wiki/Q126818","display_name":"Dimensionless quantity","level":2,"score":0.3935000002384186},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.37229999899864197},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3686000108718872},{"id":"https://openalex.org/C110639684","wikidata":"https://www.wikidata.org/wiki/Q20702","display_name":"Pendulum","level":2,"score":0.3422999978065491},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.321399986743927},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.3192000091075897},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.25619998574256897}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1140/epjd/e2017-80134-6","doi":"https://doi.org/10.1140/epjd/e2017-80134-6","is_oa":true,"landing_page_url":"https://doi.org/10.1140/epjd/e2017-80134-6","pdf_url":"https://link.springer.com/content/pdf/10.1140%2Fepjd%2Fe2017-80134-6.pdf","source":{"id":"https://openalex.org/S174148793","display_name":"The European Physical Journal D","issn_l":"1434-6060","issn":["1434-6060","1434-6079"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-1","ki-jl-1","norway-1","poland-40","russia-white-list-3"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The European Physical Journal D","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1702.08733","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1702.08733","pdf_url":"https://arxiv.org/pdf/1702.08733","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:edpsciences.org:dkey/10.1140/epjd/e2017-80134-6","doi":null,"is_oa":false,"landing_page_url":"http://www.springerlink.com/content/fulltext.pdf?id=doi:10.1140/epjd/e2017-80134-6","pdf_url":"http://www.springerlink.com/content/fulltext.pdf?id=doi:10.1140/epjd/e2017-80134-6","source":{"id":"https://openalex.org/S4306400744","display_name":"Springer Link (Chiba Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I8488066","host_organization_name":"Chiba Institute of Technology","host_organization_lineage":["https://openalex.org/I8488066"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://doi.org/10.1140/epjd/e2017-80134-6","raw_type":"Text"},{"id":"pmh:oai:pure.mpg.de:item_2404249","doi":null,"is_oa":true,"landing_page_url":"https://hdl.handle.net/11858/00-001M-0000-002C-91FB-F","pdf_url":"https://hdl.handle.net/11858/00-001M-0000-002D-89AE-3","source":{"id":"https://openalex.org/S4306400654","display_name":"MPG.PuRe (Max Planck Society)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I149899117","host_organization_name":"Max Planck Society","host_organization_lineage":["https://openalex.org/I149899117"],"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":"The European Physical Journal D","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.1702.08733","doi":"https://doi.org/10.48550/arxiv.1702.08733","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1702.08733","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":false,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.1140/epjd/e2017-80134-6","doi":"https://doi.org/10.1140/epjd/e2017-80134-6","is_oa":true,"landing_page_url":"https://doi.org/10.1140/epjd/e2017-80134-6","pdf_url":"https://link.springer.com/content/pdf/10.1140%2Fepjd%2Fe2017-80134-6.pdf","source":{"id":"https://openalex.org/S174148793","display_name":"The European Physical Journal D","issn_l":"1434-6060","issn":["1434-6060","1434-6079"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-1","ki-jl-1","norway-1","poland-40","russia-white-list-3"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The European Physical Journal D","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1596094777","display_name":null,"funder_award_id":"FR 3319/3-1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G8956946711","display_name":null,"funder_award_id":"SCHM 1202/3-1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2592318129.pdf","grobid_xml":"https://content.openalex.org/works/W2592318129.grobid-xml"},"referenced_works_count":67,"referenced_works":["https://openalex.org/W565573710","https://openalex.org/W655528169","https://openalex.org/W1521738998","https://openalex.org/W1589635682","https://openalex.org/W1647616580","https://openalex.org/W1749071620","https://openalex.org/W1968200644","https://openalex.org/W1971673222","https://openalex.org/W1971903211","https://openalex.org/W1972627917","https://openalex.org/W1975848089","https://openalex.org/W1977875944","https://openalex.org/W1978793352","https://openalex.org/W1980398563","https://openalex.org/W1981382777","https://openalex.org/W1982165208","https://openalex.org/W1988872992","https://openalex.org/W1991031176","https://openalex.org/W1992372370","https://openalex.org/W1993441285","https://openalex.org/W1994453012","https://openalex.org/W2001205788","https://openalex.org/W2001293558","https://openalex.org/W2001348549","https://openalex.org/W2003436779","https://openalex.org/W2005904988","https://openalex.org/W2012360176","https://openalex.org/W2020361634","https://openalex.org/W2023180912","https://openalex.org/W2023938011","https://openalex.org/W2028101557","https://openalex.org/W2028633797","https://openalex.org/W2040094259","https://openalex.org/W2044996661","https://openalex.org/W2047529422","https://openalex.org/W2051051688","https://openalex.org/W2051073766","https://openalex.org/W2051528453","https://openalex.org/W2055357922","https://openalex.org/W2060586413","https://openalex.org/W2066298546","https://openalex.org/W2067749522","https://openalex.org/W2073672005","https://openalex.org/W2085489032","https://openalex.org/W2090420270","https://openalex.org/W2095702170","https://openalex.org/W2102000928","https://openalex.org/W2102245148","https://openalex.org/W2102591969","https://openalex.org/W2110081819","https://openalex.org/W2112363192","https://openalex.org/W2117773375","https://openalex.org/W2122885064","https://openalex.org/W2132578448","https://openalex.org/W2157581758","https://openalex.org/W2160361725","https://openalex.org/W2259505315","https://openalex.org/W2301099622","https://openalex.org/W2462243049","https://openalex.org/W2512619855","https://openalex.org/W3016843226","https://openalex.org/W3099253083","https://openalex.org/W4213083640","https://openalex.org/W4240198074","https://openalex.org/W4256198129","https://openalex.org/W4296566866","https://openalex.org/W7070908526"],"related_works":["https://openalex.org/W2908457465","https://openalex.org/W2790202681","https://openalex.org/W4240198074","https://openalex.org/W2789071837","https://openalex.org/W2014377466","https://openalex.org/W1570671705","https://openalex.org/W4200362341","https://openalex.org/W2806964229","https://openalex.org/W2032397559","https://openalex.org/W2075704968"],"abstract_inverted_index":{"We":[0],"have":[1],"subjected":[2],"the":[3,12,16,25,55,58,62,90,94,97,119,131,138,141,147,152,162,169,175,184,208,212,218,221,225,231],"planar":[4,95],"pendulum":[5],"eigenproblem":[6],"to":[7,54,71,79,103,129,168],"a":[8,181],"symmetry":[9],"analysis":[10,46,88],"with":[11,118,217],"goal":[13],"of":[14,27,57,89,93,140,146,177,202,211,220],"explaining":[15],"relationship":[17,50],"between":[18],"its":[19,28],"conditional":[20],"quasi-exact":[21],"solvability":[22],"(C-QES)":[23],"and":[24,144,157,173,204,214,233],"topology":[26],"eigenenergy":[29,148],"surfaces,":[30],"established":[31],"in":[32,77,237],"our":[33],"earlier":[34],"work":[35],"[Front.":[36],"Phys.":[37,40,109],"Chem.":[38,39],"2,":[41],"1":[42],"(2014)].":[43],"The":[44],"present":[45],"revealed":[47],"that":[48,114],"this":[49],"can":[51],"be":[52,80,104,130],"traced":[53],"structure":[56],"tridiagonal":[59],"matrices":[60],"representing":[61],"symmetry-adapted":[63],"pendular":[64,120,213,232,243],"Hamiltonian,":[65],"as":[66,68,135,241,246],"well":[67],"enabled":[69],"us":[70],"identify":[72],"many":[73],"more":[74],"\u2013":[75,82],"40":[76],"total":[78],"exact":[81],"analytic":[83,166,178],"solutions.":[84,179],"Furthermore,":[85],"an":[86],"analogous":[87],"hyperbolic":[91],"counterpart":[92],"pendulum,":[96],"Razavy":[98,215,234,251],"problem,":[99],"which":[100,165],"was":[101],"shown":[102],"also":[105,160],"C-QES":[106,196],"[Am.":[107],"J.":[108],"48,":[110],"285":[111],"(1980)],":[112],"confirmed":[113],"it":[115,136],"is":[116],"anti-isospectral":[117],"eigenproblem.":[121],"Of":[122],"key":[123],"importance":[124],"for":[125,187,193,199,207,224],"both":[126],"eigenproblems":[127,171],"proved":[128],"topological":[132],"index":[133],"\u03ba,":[134,183,203],"determines":[137],"loci":[139],"intersections":[142],"(genuine":[143],"avoided)":[145],"surfaces":[149],"spanned":[150],"by":[151],"dimensionless":[153],"interaction":[154],"parameters":[155],"\u03b7":[156],"\u03b6.":[158],"It":[159],"encapsulates":[161],"conditions":[163],"under":[164],"solutions":[167],"two":[170],"obtain":[172],"provides":[174],"number":[176],"At":[180],"given":[182],"anti-isospectrality":[185],"occurs":[186,206],"single":[188],"states":[189,244,252],"only":[190,205],"(i.e.,":[191],"not":[192],"doublets),":[194],"like":[195],"holds":[197],"solely":[198],"integer":[200],"values":[201],"lowest":[209],"eigenvalues":[210,222],"Hamiltonians,":[216],"order":[219],"reversed":[223],"latter.":[226],"For":[227],"all":[228,249],"other":[229],"states,":[230],"spectra":[235],"become":[236],"fact":[238],"qualitatively":[239],"different,":[240],"higher":[242,250],"appear":[245],"doublets":[247],"whereas":[248],"are":[253],"singlets.":[254]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2018,"cited_by_count":3}],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2017-03-16T00:00:00"}
