{"id":"https://openalex.org/W579206236","doi":null,"title":"Waves and Oscillations: A Prelude to Quantum Mechanics","display_name":"Waves and Oscillations: A Prelude to Quantum Mechanics","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W579206236","mag":"579206236"},"language":"en","primary_location":{"id":"pmh:oai:aleph.bib-bvb.de:BVB01-028488580","doi":null,"is_oa":false,"landing_page_url":"http://search.ebscohost.com/login.aspx?direct=true&amp;scope=site&amp;db=nlebk&amp;db=nlabk&amp;AN=316640","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"software, multimedia"},"volume":null,"type":"other","is_traditional":false,"indexed_in":[],"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/A5112261562","display_name":"Walter Fox Smith","orcid":"https://orcid.org/0009-0007-9331-7486","observed_orcids":["https://orcid.org/0009-0007-9331-7486"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"W. F. Smith","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5112261562"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":17,"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/T12250","display_name":"Experimental and Theoretical Physics Studies","score":0.7656000256538391,"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/T12250","display_name":"Experimental and Theoretical Physics Studies","score":0.7656000256538391,"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":0.08100000023841858,"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.05550000071525574,"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/simple-harmonic-motion","display_name":"simple harmonic motion","score":0.9039999842643738},{"id":"https://openalex.org/keywords/damped-oscillations","display_name":"damped oscillations","score":0.8259999752044678},{"id":"https://openalex.org/keywords/forced-oscillations","display_name":"forced oscillations","score":0.8899999856948853},{"id":"https://openalex.org/keywords/resonance","display_name":"resonance","score":0.9769999980926514},{"id":"https://openalex.org/keywords/coupled-oscillators","display_name":"coupled oscillators","score":0.9399999976158142},{"id":"https://openalex.org/keywords/hilbert-spaces","display_name":"Hilbert spaces","score":0.9309999942779541},{"id":"https://openalex.org/keywords/fourier-series","display_name":"Fourier series","score":0.47200000286102295},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.6309999823570251},{"id":"https://openalex.org/keywords/wave-packets","display_name":"wave packets","score":0.3529999852180481},{"id":"https://openalex.org/keywords/heisenberg-uncertainty-principle","display_name":"uncertainty principle","score":0.46299999952316284},{"id":"https://openalex.org/keywords/quantum-wave-function","display_name":"quantum wave function","score":0.4269999861717224},{"id":"https://openalex.org/keywords/euler-s-equation","display_name":"Euler's equation","score":0.6129999756813049},{"id":"https://openalex.org/keywords/ac-circuits","display_name":"AC circuits","score":0.7080000042915344},{"id":"https://openalex.org/keywords/pendulum","display_name":"pendulum","score":0.6079999804496765},{"id":"https://openalex.org/keywords/young-s-modulus","display_name":"Young's modulus","score":0.6869999766349792},{"id":"https://openalex.org/keywords/nonlinear-oscillators","display_name":"nonlinear oscillators","score":0.7979999780654907},{"id":"https://openalex.org/keywords/chaos","display_name":"chaos","score":0.8809999823570251},{"id":"https://openalex.org/keywords/superposition","display_name":"superposition","score":0.5860000252723694},{"id":"https://openalex.org/keywords/energy-flow","display_name":"energy flow","score":0.47200000286102295},{"id":"https://openalex.org/keywords/quality-factor","display_name":"quality factor","score":0.4819999933242798},{"id":"https://openalex.org/keywords/euler-lagrange-equations","display_name":"Euler-Lagrange equations","score":0.460999995470047}],"concepts":[{"id":"https://openalex.org/C75816695","wikidata":"https://www.wikidata.org/wiki/Q835975","display_name":"Simple harmonic motion","level":2,"score":0.8031693696975708},{"id":"https://openalex.org/C40934718","wikidata":"https://www.wikidata.org/wiki/Q190070","display_name":"Harmonic oscillator","level":2,"score":0.7301596403121948},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5900675058364868},{"id":"https://openalex.org/C27753989","wikidata":"https://www.wikidata.org/wiki/Q284885","display_name":"Superposition principle","level":2,"score":0.5529197454452515},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.5362526774406433},{"id":"https://openalex.org/C2778439541","wikidata":"https://www.wikidata.org/wiki/Q7106412","display_name":"Oscillation (cell signaling)","level":2,"score":0.5083054900169373},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.44642236828804016},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.41652846336364746},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.33795464038848877},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32606959342956543},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.31676027178764343},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:aleph.bib-bvb.de:BVB01-028488580","doi":null,"is_oa":false,"landing_page_url":"http://search.ebscohost.com/login.aspx?direct=true&amp;scope=site&amp;db=nlebk&amp;db=nlabk&amp;AN=316640","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"software, multimedia"},{"id":"mag:579206236","doi":null,"is_oa":false,"landing_page_url":"http://ci.nii.ac.jp/ncid/BB03126571","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2224858799","https://openalex.org/W2028273097","https://openalex.org/W2501995469","https://openalex.org/W4300032167","https://openalex.org/W3003626899","https://openalex.org/W3012282875","https://openalex.org/W161745653","https://openalex.org/W3087764039","https://openalex.org/W3001607609","https://openalex.org/W2174597428"],"abstract_inverted_index":{"LEARNING":[0],"TOOLS":[1],"USED":[2],"IN":[3,378,431,484,489,575],"THIS":[4],"BOOK":[5],"1.":[6],"Simple":[7,94],"Harmonic":[8,95],"Motion":[9,96],"1.1":[10],"SINUSOIDAL":[11,81,472],"OSCILLATIONS":[12,82,392],"ARE":[13],"EVERYWHERE":[14],"1.2":[15],"THE":[16,64,75,143,180,187,263,302,309,357,367,371,387,394,417,429,432,439,445,467,475,539],"PHYSICS":[17],"AND":[18,27,83,87,107,114,119,122,149,158,186,204,210,213,247,259,268,282,301,340,349,407,438,457,510,524,528,538,558,562,570,581,586,597,601],"MATHEMATICS":[19],"BEHIND":[20],"SIMPLE":[21,31],"HARMONIC":[22,32,100],"MOTION":[23,33,62,235,300],"1.3":[24],"IMPORTANT":[25,72],"PARAMETERS":[26],"ADJUSTABLE":[28],"CONSTANT":[29],"OF":[30,44,53,140,155,171,201,234,254,299,333,342,441,453,517,541,588],"1.4":[34],"MASS":[35],"ON":[36,493,503],"A":[37,379],"SPRING":[38],"1.5":[39],"ELECTRICAL":[40,135,196],"OSCILLATORS":[41,116,132,136,209,267,280],"1.6":[42],"REVIEW":[43,52],"TAYLOR":[45],"SERIES":[46],"APPROXIMATIONS":[47],"1.7":[48],"EULER'S":[49],"EQUATION":[50,304,311,469],"1.8":[51],"COMPLEX":[54,57,65,73],"NUMBERS":[55],"1.9":[56],"EXPONENTIAL":[58,138],"NOTATION":[59,261],"FOR":[60,67,99,183,307,323,345,386,401,478,550,556,565,572,583,609],"OSCILLATORY":[61],"1.10":[63],"REPRESENTATION":[66],"AC":[68],"CIRCUITS":[69],"1.11":[70],"ANOTHER":[71],"FUNCTION:":[74],"QUANTUM":[76],"MECHANICAL":[77,131,551],"WAVEFUNCTION":[78],"1.12":[79],"PURE":[80],"UNCERTAINTY":[84],"PRINCIPLES":[85],"CONCEPT":[86,121,157,212,281,348,406,456,527,600],"SKILL":[88,123,159,214,283,350,408,458,529,602],"INVENTORY":[89,124,160,215,284,351,409,459,530,603],"PROBLEMS":[90,125,161,216,285,352,410,460,531,604],"2.":[91],"Examples":[92],"of":[93],"2.1":[97],"REQUIREMENTS":[98],"OSCILLATION":[101],"2.2":[102],"PENDULUMS":[103],"2.3":[104],"ELASTIC":[105],"DEFORMATIONS":[106],"YOUNG'S":[108],"MODULUS":[109],"2.4":[110],"SHEAR":[111],"2.5":[112],"TORSION":[113],"TORSIONAL":[115],"2.6":[117],"BENDING":[118],"CANTILEVERS":[120],"3.":[126],"Damped":[127],"oscillations":[128],"3.1":[129],"DAMPED":[130,134,151],"3.2":[133],"3.3":[137],"DECAY":[139],"ENERGY":[141,174,270],"3.4":[142],"QUALITY":[144],"FACTOR":[145],"3.5":[146],"UNDERDAMPED,":[147],"OVERDAMPED,":[148],"CRITICALLY":[150],"BEHAVIOR":[152],"3.6":[153],"TYPES":[154],"DAMPING":[156,172],"4.":[162],"Driven":[163],"Oscillations":[164],"and":[165,221,290],"Resonance":[166],"4.1":[167],"RESONANCE":[168,197],"4.2":[169],"EFFECTS":[170],"4.3":[173],"FLOW":[175],"4.4":[176],"LINEAR":[177],"DIFFERENTIAL":[178],"EQUATIONS,":[179],"SUPERPOSITION":[181,476],"PRINCIPLE":[182,477],"DRIVEN":[184,278],"SYSTEMS,":[185],"RESPONSE":[188],"TO":[189,376],"MULTIPLE":[190],"DRIVE":[191],"FORCES":[192],"4.5":[193],"TRANSIENTS":[194],"4.6":[195],"4.7":[198],"OTHER":[199,205],"EXAMPLES":[200],"RESONANCE:":[202],"MRI":[203],"SPECTROSCOPIES":[206],"4.8":[207],"NON-LINEAR":[208],"CHAOS":[211],"5.":[217],"Symmetric":[218],"coupled":[219,288],"oscillators":[220,289],"Hilbert":[222],"space":[223],"5.1":[224],"BEATS:":[225],"AN":[226,251,610],"ASIDE?":[227],"5.2":[228],"TWO":[229,317],"SYMMETRIC":[230],"COUPLED":[231,266,279],"OSCILLATORS:":[232],"EQUATIONS":[233,298],"5.3":[236],"NORMAL":[237,241,244,248,320,334,336,383,398,577],"MODES":[238,242,249],"5.4":[239],"SUPERPOSING":[240],"5.5":[243],"MODE":[245,321,337,384,399],"ANALYSIS,":[246],"AS":[250],"ALTERNATE":[252],"DESCRIPTION":[253],"REALITY":[255],"5.6":[256],"HILBERT":[257,343],"SPACE":[258,344],"BRA-KET":[260],"5.7":[262],"ANALOGY":[264],"BETWEEN":[265],"MOLECULAR":[269],"LEVELS":[271],"5.8":[272],"NON-ZERO":[273],"INITIAL":[274],"VELOCITIES":[275],"5.9":[276],"DAMPED,":[277],"6.":[286],"Asymmetric":[287],"the":[291],"eigenvalue":[292],"equation":[293],"6.1":[294],"MATRIX":[295,329],"MATH":[296,330],"6.2":[297],"EIGENVALUE":[303,310],"6.3":[305],"PROCEDURE":[306],"SOLVING":[308],"6.4":[312],"SYSTEMS":[313,326,403,552],"WITH":[314],"MORE":[315,328],"THAN":[316],"OBJECTS":[318],"6.5":[319],"ANALYSIS":[322,385,400,455],"MULIT-OBJECT,":[324],"ASYMMETRICAL":[325],"6.6":[327],"6.7":[331],"ORTHOGONALITY":[332],"MODES,":[335],"COORDINATES,":[338],"DEGENERACY,":[339],"SCALING":[341],"UNEQUAL":[346],"MASSES":[347],"7.":[353],"String":[354],"theory":[355],"7.1":[356],"BEADED":[358,388],"STRING":[359,389,396],"7.2":[360],"STANDING":[361],"WAVE":[362,468],"GUESS:":[363],"BOUNDARY":[364,542],"CONDITIONS":[365,543],"QUANTIZE":[366],"ALLOWED":[368],"FREQUENCIES":[369],"7.3":[370],"HIGHEST":[372],"POSSIBLE":[373],"FREQUENCY":[374,443],"CONNECTION":[375],"WAVES":[377,473,480,483,488,492,498,512,519,546,564,574,599],"CRYSTALLINE":[380],"SOLID":[381],"7.4":[382],"7.5":[390],"LONGITUDINAL":[391],"7.6":[393],"CONTINUOUS":[395,402],"7.7":[397],"7.8":[404],"K-SPACE":[405],"8.":[411],"Fourier":[412],"analysis":[413],"8.1":[414],"INTRODUCTION":[415,465],"8.2":[416],"FOURIER":[418,433,436,447,454],"EXPANSION":[419,434],"8.3":[420],"EXPANSIONS":[421],"USING":[422],"NON-NORMALIZED":[423],"ORTHOGONAL":[424],"BASIS":[425],"FUNCTIONS":[426],"8.4":[427],"FINDING":[428],"COEFFICIENTS":[430],"8.5":[435],"TRANSFORMS":[437],"MEANING":[440],"NEGATIVE":[442],"8.6":[444],"DISCRETE":[446],"TRANSFORM":[448],"(DFT)":[449],"8.7":[450],"SOME":[451],"APPLICATIONS":[452],"9.":[461],"Traveling":[462],"waves":[463],"9.1":[464],"9.2":[466],"9.3":[470],"TRAVELING":[471,479],"9.4":[474],"9.5":[481],"ELECTROMAGNETIC":[482,487,511,573],"VACUUM":[485],"9.6":[486],"MATTER":[490],"9.7":[491],"TRANSMISSION":[494,557,566,571,582],"LINES":[495,567],"9.8":[496],"SOUND":[497,518,584],"9.9":[499],"MUSICAL":[500],"INSTRUMENTS":[501],"BASED":[502],"TUBES":[504],"9.10":[505],"POWER":[506],"CARRIED":[507],"BY":[508],"ROPE":[509],"RMS":[513],"AMPLITUDES":[514],"9.11":[515],"INTENSITY":[516],"DECIBELS":[520],"9.12":[521],"DISPERSION":[522],"RELATIONS":[523],"GROUP":[525,607],"VELOCITY":[526,608],"10.":[532],"Waves":[533],"at":[534],"interfaces":[535],"10.1":[536],"REFLECTIONS":[537],"IDEA":[540],"10.2":[544],"TRANSMITTED":[545,563],"10.3":[547],"CHARACTERISTIC":[548],"IMPEDANCES":[549],"10.4":[553],"UNIVERSAL":[554],"EXPRESSIONS":[555],"REFLECTION":[559,569,580,596],"10.5":[560],"REFLECTED":[561],"10.6":[568],"MATTER:":[576],"INCIDENCE":[578],"10.7":[579],"WAVES,":[585],"SUMMARY":[587],"ISOMORPHISMS":[589],"10.8":[590],"SNELL'S":[591],"LAW":[592],"10.9":[593],"TOTAL":[594],"INTERNAL":[595],"EVANESCENT":[598],"APPENDIX":[605],"A:":[606],"ARBITRARY":[611],"ENVELOPE":[612],"FUNCTION":[613],"INDEX":[614]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2}],"updated_date":"2026-10-25T09:29:13.331239","created_date":"2016-06-24T00:00:00"}
