{"id":"https://openalex.org/W7212004195","doi":"https://doi.org/10.48550/arxiv.2609.07505","title":"Stationary states for a particle in a box with slanted walls","display_name":"Stationary states for a particle in a box with slanted walls","publication_year":2026,"publication_date":"2026-09-07","ids":{"openalex":"https://openalex.org/W7212004195","doi":"https://doi.org/10.48550/arxiv.2609.07505"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.07505","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.07505","pdf_url":"https://arxiv.org/pdf/2609.07505","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"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.07505","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5045749428","display_name":"Nivaldo Agostinho Lemos","orcid":"https://orcid.org/0000-0002-2386-1247","observed_orcids":["https://orcid.org/0000-0002-2386-1247"]},"institutions":[{"id":"https://openalex.org/I161127581","display_name":"Universidade Federal Fluminense","ror":"https://ror.org/02rjhbb08","country_code":"BR","type":"education","lineage":["https://openalex.org/I161127581"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"Lemos, Nivaldo A.","raw_affiliation_strings":["Instituto de F\u00edsica -Universidade Federal Fluminense Av. Litor\u00e2nea s /n , Boa Viagem , 24210-340 , Niter\u00f3i -RJ , Brasil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto de F\u00edsica -Universidade Federal Fluminense Av. Litor\u00e2nea s /n , Boa Viagem , 24210-340 , Niter\u00f3i -RJ , Brasil","institution_ids":["https://openalex.org/I161127581"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5045749428"],"corresponding_institution_ids":["https://openalex.org/I161127581"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"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":0.4787999987602234,"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":0.4787999987602234,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.19130000472068787,"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":0.11259999871253967,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/particle-in-a-box","display_name":"particle in a box","score":0.9769999980926514},{"id":"https://openalex.org/keywords/infinite-potential-well","display_name":"infinite potential well","score":0.8830000162124634},{"id":"https://openalex.org/keywords/airy-functions","display_name":"Airy functions","score":0.7570000290870667},{"id":"https://openalex.org/keywords/energy-eigenvalues","display_name":"energy eigenvalues","score":0.8119999766349792},{"id":"https://openalex.org/keywords/transcendental-equations","display_name":"transcendental equations","score":0.9319999814033508},{"id":"https://openalex.org/keywords/bohr-correspondence-principle","display_name":"Bohr correspondence principle","score":0.9279999732971191},{"id":"https://openalex.org/keywords/classically-forbidden-region","display_name":"classically forbidden region","score":0.8769999742507935},{"id":"https://openalex.org/keywords/ground-state","display_name":"ground state","score":0.6499999761581421},{"id":"https://openalex.org/keywords/quantum-mechanics-education","display_name":"quantum mechanics education","score":0.5289999842643738}],"concepts":[{"id":"https://openalex.org/C197806323","wikidata":"https://www.wikidata.org/wiki/Q909221","display_name":"Particle in a box","level":3,"score":0.7940999865531921},{"id":"https://openalex.org/C140901224","wikidata":"https://www.wikidata.org/wiki/Q409415","display_name":"Airy function","level":2,"score":0.6703000068664551},{"id":"https://openalex.org/C47458137","wikidata":"https://www.wikidata.org/wiki/Q911951","display_name":"Stationary state","level":2,"score":0.6565999984741211},{"id":"https://openalex.org/C69523127","wikidata":"https://www.wikidata.org/wiki/Q4480008","display_name":"Ground state","level":2,"score":0.5730999708175659},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5687999725341797},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5181999802589417},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.48030000925064087},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.474700003862381},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.4537000060081482},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.45170000195503235},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.45159998536109924},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.4374000132083893},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4072999954223633},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4066999852657318},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.3946000039577484},{"id":"https://openalex.org/C2778517922","wikidata":"https://www.wikidata.org/wiki/Q7140482","display_name":"Particle (ecology)","level":2,"score":0.37770000100135803},{"id":"https://openalex.org/C84551667","wikidata":"https://www.wikidata.org/wiki/Q155640","display_name":"Potential energy","level":2,"score":0.34850001335144043},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.3398999869823456},{"id":"https://openalex.org/C40934718","wikidata":"https://www.wikidata.org/wiki/Q190070","display_name":"Harmonic oscillator","level":2,"score":0.33820000290870667},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.32690000534057617},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.31690001487731934},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31290000677108765},{"id":"https://openalex.org/C139609574","wikidata":"https://www.wikidata.org/wiki/Q2273509","display_name":"Transcendental equation","level":3,"score":0.2953999936580658},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.29089999198913574},{"id":"https://openalex.org/C28855332","wikidata":"https://www.wikidata.org/wiki/Q198099","display_name":"Quantization (signal processing)","level":2,"score":0.28299999237060547},{"id":"https://openalex.org/C64642268","wikidata":"https://www.wikidata.org/wiki/Q230937","display_name":"State function","level":2,"score":0.27900001406669617},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.2728999853134155},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.2728999853134155},{"id":"https://openalex.org/C2983197053","wikidata":"https://www.wikidata.org/wiki/Q654182","display_name":"Energy spectrum","level":2,"score":0.2680000066757202},{"id":"https://openalex.org/C63036615","wikidata":"https://www.wikidata.org/wiki/Q165498","display_name":"Schr\u00f6dinger equation","level":2,"score":0.26750001311302185},{"id":"https://openalex.org/C29373527","wikidata":"https://www.wikidata.org/wiki/Q753658","display_name":"Subharmonic function","level":2,"score":0.25839999318122864},{"id":"https://openalex.org/C8171440","wikidata":"https://www.wikidata.org/wiki/Q903414","display_name":"Steady state (chemistry)","level":2,"score":0.25130000710487366},{"id":"https://openalex.org/C98184364","wikidata":"https://www.wikidata.org/wiki/Q1780131","display_name":"Argument (complex analysis)","level":2,"score":0.25099998712539673}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.07505","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.07505","pdf_url":"https://arxiv.org/pdf/2609.07505","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":"doi:10.48550/arxiv.2609.07505","doi":"https://doi.org/10.48550/arxiv.2609.07505","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.07505","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.07505","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.07505","pdf_url":"https://arxiv.org/pdf/2609.07505","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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7212004195.pdf","grobid_xml":"https://content.openalex.org/works/W7212004195.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4225156083","https://openalex.org/W2058039605","https://openalex.org/W4392281363","https://openalex.org/W4250566106","https://openalex.org/W6889608680","https://openalex.org/W153771761","https://openalex.org/W2903681133","https://openalex.org/W7134860917","https://openalex.org/W1609888472","https://openalex.org/W1966656660"],"abstract_inverted_index":{"The":[0,17,50],"quantum":[1,57],"mechanical":[2],"problem":[3,209],"of":[4,30,70,80,91,108,130,166,179,230],"a":[5,8,23,95,113,149,187],"particle":[6,111,133],"in":[7,105,112,134],"infinite":[9],"potential":[10],"well":[11],"with":[12,153,212,218],"slanted":[13],"walls":[14,178],"is":[15,100,121,146,151,162,194],"studied.":[16],"energy":[18,61,72],"eigenvalues":[19],"are":[20,37,43],"determined":[21],"by":[22,45,78,86],"transcendental":[24],"equation":[25],"involving":[26],"the":[27,31,40,59,71,106,109,116,123,126,128,132,135,143,154,159,163,171,191,197,213,226],"Airy":[28,92,219],"function":[29],"first":[32],"kind.":[33],"Two":[34],"limiting":[35],"cases":[36,107],"discussed.":[38],"Next,":[39],"allowed":[41],"energies":[42],"found":[44],"graphical":[46,51],"and":[47,84,148,176,202],"numerical":[48],"methods.":[49],"analysis":[52],"hints":[53],"that":[54],"for":[55,157],"large":[56],"numbers":[58],"consecutive":[60],"levels":[62],"get":[63,216],"arbitrarily":[64],"close":[65],"together.":[66],"This":[67],"asymptotic":[68],"behavior":[69],"spectrum":[73],"actually":[74],"holds,":[75],"as":[76],"shown":[77],"means":[79],"an":[81],"intuitive":[82],"argument":[83],"confirmed":[85],"resorting":[87],"to":[88,215,225],"basic":[89],"properties":[90],"functions.":[93],"In":[94,170],"sense,":[96],"Bohr's":[97],"correspondence":[98],"principle":[99],"more":[101,124],"accurately":[102],"fulfilled":[103],"than":[104],"standard":[110,227],"box":[114],"or":[115],"harmonic":[117,155],"oscillator.":[118],"A":[119],"state":[120,161,193],"regarded":[122],"confined":[125,165,199],"less":[127],"probability":[129],"finding":[131],"classically":[136],"forbidden":[137],"region.":[138],"For":[139],"some":[140],"stationary":[141,168],"states":[142],"confinement":[144],"degree":[145],"calculated":[147],"comparison":[150],"made":[152],"oscillator,":[156],"which":[158,221],"ground":[160,192],"least":[164,198],"all":[167],"states.":[169],"symmetric":[172],"case":[173],"---":[174,182],"right":[175],"left":[177],"equal":[180],"slope":[181,190],"something":[183],"unexpected":[184],"happens:":[185],"beyond":[186],"certain":[188],"critical":[189],"no":[195],"longer":[196],"eigenstate.":[200],"Over":[201],"above":[203],"its":[204],"interesting":[205],"physical":[206],"features,":[207],"this":[208],"provides":[210],"students":[211],"opportunity":[214],"acquainted":[217],"functions,":[220],"do":[222],"not":[223],"belong":[224],"mathematical":[228],"repertoire":[229],"physics":[231],"undergraduates.":[232]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-09-10T00:00:00"}
