
kwaandam mechanics

aattangaludeyum upa aattomik kanangaludeyum alavil prakrithiyude bhauthika gunangalekkurichu vivaranam nalkunna bhauthikashaasthrathile oru adisthaana sidhaanthamaanu kwaandam mechanics. kwaandam rasathanthram, kwaandam feeld sidhaantham, kwaandam saankethikavidya, kwaandam information sayans ennivayulppede ellah kwaandam bhouthikashaasthrathinteyum aditharayaanithu.
kwaandam mekkaaniksinte varavinu munbu nilaninnirunna sidhaanthangalude shekharamaaya classical physics, prakrithiyude pala vashangaleyum oru saadhaarana (macroscopic) skailil vivarikkunnu, pakshe avaye cheria (aattomik, sub aattomik) skeyilukalil vivarikkan paryaapthamalla. classical physixile mikka sidhaanthangalum valia (macroscopic) skailil saadhuthayulla oru ekadesha kanakkayi kwaandam mechanicsil ninnu uruthirinjathaanu.
kwaandam mechanics classical physixil ninnu vyathyasthamaan, oorjjam, momentam, angular momentam, oru boundu sisttathinte mattu alavukal enniva vyathiriktha moolyangalil (quandisation) parimithappedutthiyirikku; vasthukkalkk kanangaludeyum tharamgangaludeyum (taranga-kanika duvality) savisheshathakalundu; koodaathe oru bhauthika alavinte moolyam athinte alavinu munbu ethra krithyamaayi pravachikkaan kazhiyum ennathinu parimithikalundu, poornnamaaya prarambha vyavasthakal (anishchithathva thathwam) nalkunnu.
1900-ll black body radiation prashnathinulla maiks plaankinte pariharam, 1905-leeii albert ainsteente pepparile oorjjavum aavruthiyum thammilulla anuroopam enniva polulla classical physixumaayi poruthappedutthaan kazhiyaatha nireekshanangal vishadeekarikkunnathinaayi sidhaanthangalil ninnaan kwaandam mechanics kramena uyarnnuvannathu. ippol "pazhaya kwaandam sidhaantham" ennariyappedunna microscopic prathibhasangal manasilakkaanulla eee aadyakaala sramangal 1920 kalude madhyathil neels booar, ervin shroadinger, verner heisenberg, maiks boonn, pooll dirac thudangiyavar kwaandam mekkaaniksinte poornna vikasanathilekku nayichu. prathyekamaayi vikasippichedutha vividha ganithashaasthra aupachaarikathakalilaanu aadhunika sidhaantham roopappeduthiyittullathu. avayilonnil, tharamgapravartthanam ennu vilikkunna oru ganithashaasthra ghadakam, oru kanikayude oorjjam, aakkam, mattu bhauthika gunangal ennivayude alavukal enthokke nalkum ennathinekkurichulla vivarangal probability aamplityoodukalude roopathil nalkunnu.
avalokanavum adisthaana ashayangalum.
bhauthika samvidaanangalude gunangalum perumattavum kanakkakkaan kwaandam mechanics anuvadikkunnu. ithu saadhaaranayaayi microscopic sisttangalil prayogikkunnu thanmathrakal, attangal, sub-aattomik kanikakal. aayirakkanakkin attangalulla sankeernamaaya thanmaathrakale ithu nilanirthunnuvennu theliyikkappettittund, ennaal manushyaril ithu prayogikkunnathu vignarude suhruthu polulla daarshanika prasnangal uyarthunnu, mathramalla prapanchatthil mothatthil ithu prayogikkunnathu oohaapohangalaayi thudarunnu. kwaandam mekkaaniksinte pravachanangal pareekshanaathmakamaayi valare uyarnna alavilulla krithyathayode parishodhichittundu.
enthaanu sambhavikkuka ennu saadhaaranayaayi urappode pravachikkaan kazhiyilla, marichu saadhyathakal maathrame nalkoo ennathaanu sidhaanthathinte adisthaana savisheshatha. ganithashaasthraparamaayi, probability amplitude ennariyappedunna oru sankeernna samkhyayude kevala moolyathinte chathuram edukkunnathiloodeyaanu probability kandethunnathu. bhauthikashaasthranjanaaya maiks boonn ennayaalude perilulla boonn ruul ennaanu ithu ariyappedunnathu. udaaharanathinu, oru electron polulla oru kwaandam kanikaye oru tharamgapravartthanam upayogichu vivarikkaam, ithu bahiraakaashathe oro pooyintumaayum oru probability aamplityoodumaayi bandhappeduthunnu. eee aamplityoodukalil boonn ruul prayogikkunnathu alakkaan oru pareekshanam nadathumbol electroninu undaakunna sthaanathinu oru probability density function nalkunnu. sidhaanthathinu cheyyaan kazhiyunna ettavum mikachathaanu ithu; electron evide kandethumennu krithyamaayi parayaan kazhiyilla. shroadinger samavaakyam oru nimishavumaayi bandhapetta probability aamplityoodukalude shekharathe mattonninumayi bandhapetta probability aamplityoodukalude shekharavumaayi bandhappettirikkunnu.
alakkaavunna vyathyastha alavukal thammilulla pravachanaatheethayile oru kaimattamaanu kwaandam mekkaaniksinte ganithashaasthra niyamangalude oru anantharafalam. eee anishchithathva thathwathinte ettavum prashasthamaaya roopam parayunnath oru kwaandam kanika engane thayyarakkiyalum allengil athil ethra shradhaapoorvvam pareekshanangal krameekarichaalum, athinte sthaanam alakkunnathinum athe samayam athinte vegatha alakkunnathinum krithyamaaya pravachanam nadathunnathu asaadyamaanu ennaanu.
kwaandam mekkaaniksinte ganithashaasthra niyamangalude mattoru anantharafalamaanu kwaandam interference prathibhasam, ithu palappozhum double-slitt pareekshanatthiloode chithreekarikkunnu. eee pareekshanatthinte adisthaana pathippil, lazer beam polulla oru yojicha prakasha srothass, rund samanthara slittukalaal thulachukayariya oru plettine prakashippikkunnu, koodaathe slittukaliloode kadannupokunna prakasham plettinu pinnilulla screenil nireekshikkappedunnu. prakaashatthinte taranga swabhaavam rund cheettukaliloode kadannupokunna prakaashatharamgangale thadassappeduthukayum screenil thilakkamullathum irundathumaaya baandukal srishtikkukayum cheiyunnu-prakasham classical kanikakal ulkkollunnuvenkil pratheekshikkappedaatha oru phalam. ennirunnaalum, tharamgangalekkaal vyakthigatha kanangalayi prakasham ellaayppozhum screenil vyathiriktha pooyintukalil agiranam cheyyappedunnuvennu kandethiyittundu; screenil eee kanangalude vyathyastha saandrathayiloode edapedal paatten prathyakshappedunnu. koodaathe, slittukalile dittaktarukal ulppedunna pareekshanatthinte pathippukal kandethunnathu oro photone oru slittiloodeyaanu kadannupokunnathu (oru classical kanika pole), rund slittukaliloodeyalla (oru tharamgam pole). ennirunnaalum, eathu pilarppiloodeyaanu kanikakal kadannupokunnathennu kandethiyaal avaa edapedal paatten roopappeduthillennu atharam pareekshanangal theliyikkunnu. electronukal polulla mattu aattomik skeyil entittikal eratta slittilekku vedivaykkumbol athe swabhaavam prakadippikkunnathaayi kaanapedunnu. eee swabhaavathe taranga-kanika dwaithatha ennu vilikkunnu.
kwaandam mechanics pravachicha mattoru ethir-avabodhajanya prathibhaasamaan kwaandam tunneling oru pottensial barrierinu ethire pookunna oru kanikaykku athinte gathikorjjam pottanshyalinte paramavadhi valuppathekkaal cheruthaanenkilum athu kadakkaan kazhiyum. classical mechanicsil eee kanika kudungikkidakkum. radio active kshayam, nakshathrangalile nuclear fusion, scanning tunneling microscopy, tunnel diode thudangiya prayogangal enniva prapthamaakkunna niravadhi pradhana prathyaaghaathangal kwaandam tunnelinginu undu.
kwaandam sisttangal edapedumbol, athinte phalam kwaandam entaamgilmentinte srishtiyaayirikkaam avayude gunangal parasparam bandhappettirikkunnathil oro bhaagathinteyum adisthaanathil maathram avayekkurichu oru vivaranam inii saadhyamalla. ervin shroadinger entanglent ennu vilikkunnu..."kwaandam mekkaaniksinte savishesha swabhaavam, classical chinthaadhaarakalil ninnulla athinte muzhuvan vyathichalanavum nadappilaakkunnu". kwaandam entaamgilment kwaandam suedo-telepathy ethir-avabodhajanyamaaya gunangale prapthamaakkunnu, koodaathe kwaandam qee vitharanam, superdense coding thudangiya ashayavinimaya protocolukalil ithu oru moolyavathaaya vibhavamaakaam. janakeeyamaaya thettidhaaranaykku virudhamaayi, aashayavinimayamillaatha sidhaantham theliyikkunnathupole, prakaashathekkaal vegathil signalukal ayaykkaan keniyil anuvadikkunnilla.
kwaandam sidhaanthathil thanne abhisambodhana cheythirikkunna alavukalekkaal adisthaanaparamaaya saangalppika gunangalaya "maranjirikkunna variableukal" parisodhikkuka ennathaanu entaamgilment vazhi thurakkunna mattoru saadhyatha, ithinekkurichulla arivu kwaandam sidhaanthathinu nalkaan kazhiyunnathinekkaal kooduthal krithyamaaya pravachanangal anuvadikkum. phalangalude oru shekharam, ettavum sradheyamaaya bell sidhaantham, atharam maranjirikkunna-variable sidhaanthangalude vishalamaaya klaasukal vaasthavathil kwaandam physixumaayi poruthappedunnillenna theliyichittundu. bell sidhaanthamanusarichu, prakrithi yadhaarthathil "local" hiden veriyabilukalude eathenkilum sidhaanthathinu anusrithamaayi pravartthikkunnundel, oru bell testtinte phalangal oru prathyeka, alakkaavunna reethiyil parimithappedutthum. ketturappulla kanikakal upayogichu niravadhi bell testtukal nadathiyittundu, praadeshika maranjirikkunna variableukal chumathunna niyanthranangalumaayi poruthappedaattha phalangal avaa kaanichu.
ulppettirikkunna yadhaartha ganithashaasthram avatharippikkathe eee ashayangal upariplavamaaya reethiyil avatharippikkan kazhiyilla; kwaandam mechanics manasilakkaan sankeernna samkhyakal kaikaaryam cheyyuka mathramalla, leanier aljibra, deferential samavaakyangal, group sidhaantham, mattu noothana vishayangal ennivayum aavasyamaanu. athanusarichu, eee lekhanam kwaandam mekkaaniksinte oru ganitha roopeekaranam avatharippikkukayum upayogapradavum palappozhum padichathumaaya chila udaaharanangalil athinte prayogam sarway cheyyukayum cheyyum.
ganithashaasthra roopeekaranam.
kwaandam mekkaaniksinte ganithashaasthraparamaayi karsanamaaya roopeekaranathil, oru kwaandam mechanical sisttathinte avastha oru (verthirikkaavunna) sankeernamaaya hilbert space formula 2-ll ulppedunna oru vekttar formulayanu. eee vekttar hilbert space innar prodakttinu keezhil normalise cheyyappedumennu anumaanikkappedunnu, athaayath, ithu formula 3 anusarikkunnu, koodaathe ithu sankeernamaaya modulus 1 (aagola ghattam) vare nannayi nirvachikkappettittundu, athaayath, formula 1 umm formula 5 umm ore bhauthika samvidaanathe prathinidheekarikkunnu. mattoru vidhathil paranjaal, saadhyamaaya avasthakal saadhaaranayaayi sankeernamaaya projective space ennu vilikkunna hilbert spacinte projective spacile poyintukalaanu. eee hilbert spacinte krithyamaaya swabhaavam systethe aasrayichirikkunnu-udaaharanathinu, sthaanavum aavegavum vivarikkunnathin hilbert space sankeernamaaya square-integrable functionukalude formula _ 6 aanu, athesamayam orotta protoninte spinninte hilbert space saadhaarana aantharika uthppannathodoppam dvimaana sankeernna vector formula _ 7 nte space maathramaan.
hilbert spacil pravartthikkunna hermissian (kooduthal krithyamaayi paranjaal, svayam-adjayint) leanier oopparettarmaaraaya nireekshanavasthukkal prathinidheekarikkunna thaalpparya sthaanam, aakkam, oorjjam, spin ennivayude bhauthika alavukal. oru kwaandam avastha oru nireekshikkaavunnathinte eejanvektar aakam, eee saahacharyathil athine eejanstettu ennu vilikkunnu, anubandha eejan moolyam aaa eejanstettil nireekshikkaavunnathinte moolyavumaayi poruthappedunnu. kooduthal pothuve, oru kwaandam avastha kwaandam superposition ennariyappedunna aiganstettukalude oru rekheeya samyojanamayirikkum. oru nireekshikkaavunna alavu alakkumbol, phalam boonn ruul nalkunna probabilityulla athinte eejan moolyangalilonnaayirikkum ettavum lalithamaaya saahacharyathil eejan value formula _ 8 degenerate allaathathum probability formula _ 9 nalkunnathumaanu, ivide formula _ 10 athinte anubandha eejanvektaraanu. kooduthal pothuve, eejan value degenerate aanu, probability formula _ 11 nalkunnu, ivide formula _ 12 athinte anubandha eejanspesil projectoraan. thudarchayaaya saahacharyathil, eee soothravaakyangal pakaram probability density nalkunnu.
alaveduppinushesham, phalam formula _ 8 labhichenkil, kwaandam avastha formula _ 10 lake, degenerate cheyyaatha saahacharyathil, allengil formula _ 15 lake, pothuvaaya saahacharyathil, thakarumennu anumaanikkappedunnu. athinaal kwaandam mekkaaniksinte probabilistik swabhaavam alaveduppinte pravartthanatthil ninnaan uthbhavikkunnath. kwaandam sisttangalude manassilakkaan ettavum budhimuttulla vashangalilonnaanith. prashasthamaaya booar-ainsteen samvaadangalile kendra vishayamaayirunnu ithu, athil rund shaasthranjarum chinta pareekshanangaliloode eee adisthaana thathwangal vyakthamakkaan shramichu. kwaandam mekkaaniksinte roopeekaranathinu sheshamulla pathittaandukalil, oru "alavu" enthaanenna chodyam vishadamaayi padikkappettittund. tharamgapravartthana thakarcha" enna ashayam illaathaakkunna kwaandam mekkaaniksinte puthiya vyaakhyaanangal roopappeduthiyittundu (udaaharanathinu, bahu-loka vyaakhyaanam kaanuka). oru kwaandam sisttam oru alakkal upakaranavumayi samvadikkumbol, avayude athath taranga pravartthanangal ketturappilakukayum angane yadhaartha kwaandam sisttam oru swatantra entittiyaayi nilanilkkunnath avasaanikkukayum cheiyunnu ennathaanu adisthaana ashayam. vishadaamshangalkku, kwaandam mechanicsile alaveduppinekkurichulla lekhanam kaanuka.
oru kwaandam avasthayude samaya parinaamatthe shroadinger samavaakyam vivarikkunnu
ivide soothravaakyam _ 17 ennathu sisttathinte motham oorjjavumaayi bandhapetta nireekshikkaavunna hamiltonian, formula _ 18 ennathu reduced plank konsttant ennivaye soochippikkunnu. kwaandam systethe oru classical sisttam upayogichu ekadeshamaayi kanakkakkaan kazhiyunna sandarbhangalil hamiltonian classical hamiltonianaayi churukkunnathinayi sthiramaaya formula _ 19 avatharippikkunnu; chila paridhikalil atharamoru ekadesha kanakk undakkaanulla kazhivine correspondence thathwam ennu vilikkunnu.
eee deferential samavaakyathinte pariharam nalkunnathu
oopparettar formula _ 21 time-evalution oopparettar ennariyappedunnu, koodaathe ithu ekathaanamaanenna nirnaayaka savisheshathayundu. eee samaya parinamam nirnnaayakamaan, athaayath-oru prarambha kwaandam avastha soothravaakyam _ 22 nalkiyaal-kwaandam avastha soothravaakyam _ 23 pinneedu eppol venamenkilum enthaayirikkumennu ithu oru krithyamaaya pravachanam nadathunnu.
hamiltonian aijanstettukal pole chila tharamgapravartthanangal samayathil ninnu swathanthramaaya probability vitharanangal srishtikkunnu. classical mechanicsil chalanathmakamaayi pariganikkunna niravadhi samvidaanangale atharam "staatik" taranga pravartthanangal vivarikkunnu. udaaharanathinu, aaveshabharithamallaatha oru aattathile orotta electronine aattomik nucleusinu chuttum vrithaakrithiyilulla sanjaarapathathil neengunna oru kanikayaayi classicalaayi chithreekarikkunnu, athesamayam kwaandam mechanicsil, nucleusinu chuttumulla oru staatik taranga pravarthanamaanu ithine vivarikkunnath. udaaharanathinu, aaveshabharithamallaatha hydrajan aattathinte electron taranga pravartthanam oru "s" oorbittal () ennariyappedunna golaakrithiyilulla samamithiyaan.
kwaandam harmonic oosilettar, oru boxile kanika, dihydrajan kaatteshan, hydrajan aattam ennivayulppede thaarathamyena lalithamaaya hamiltonian modalukalkk shroadinger samavaakyathinte vishakalana pariharangal ariyappedunnu. rund electronukal maathram adangiya healium aattam polum poornnamaayum vishakalana chikilsaykkulla ellah sramangaleyum ethirthu.
ennirunnaalum, ekadesha pariharangal kandethunnathinulla saankethikavidyakalundu. perterbation sidhaantham ennu vilikkunna oru reethi, oru lalithamaaya kwaandam mechanical modalinte vishakalana phalam upayogichu (udaaharanathinu) durbalamaaya pottensial energy cherthu anubandhavum ennaal kooduthal sankeernavumaaya modalinu oru phalam srishtikkunnu. mattoru reethiye "semi-classical ekweshan oof moshan" ennu vilikkunnu, ithu kwaandam mechanics classical perumaattatthil ninnu cheria vyathiyanangal maathram srishtikkunna samvidaanangalkku baadhakamaan. classical chalanathe adisthaanamaakki eee vyathiyanangal kanakkakkaam. kwaandam araajakathva mekhalayil eee sameepanam prathyekichum pradhaanamaan.
anishchithathva thathwam.
adisthaana kwaandam aupachaarikathayude oru anantharafalamaanu anishchithathva thathwam. oru kwaandam kanikayude oru thayyaareduppinum athinte sthaanam alakkunnathinum athinte aakkam alakkunnathinum oresamayam krithyamaaya pravachanangal soochippikkaan kazhiyillennu athinte ettavum parichithamaaya roopathil ithu prasthaavikkunnu. sthaanavum aavegavum nireekshikkaavunnavayaan, athaayath avaye prathinidheekarikkunnath hermissian oopparettarmaaraanu. position oopparettar formula _ 24 umm momentam oopparettar formula _ 25 umm yaatra cheiyunnilla, marichu canonical commutation bandhathe thripthippeduthunnu
oru kwaandam avastha nalkiyaal, boonn ruul formula _ 27, formula _ 28 ennivayude prathekshikkunna moolyangal kanakkakkaanum koodaathe avayude shakthikalkkum kanakkakkaanum namme anuvadikkunnu. nirvvachikkuka 
oru staanderd deviation vazhi nireekshikkaavunna oru anishchithathvam, namukk undu
athupole thanne aakkam
anishchithathva thathwam parayunnu
onnukil staanderd deviation thathwathil ekapaksheeyamaayi cheruthayirikkaam, pakshe randum oresamayam allah. eee asamathvam svayam-adjayint oopparettarmaarude formula _ 32, formula _ 33 ennivayude ekapaksheeya jodikalilekku saamaanyavalkkarikkappedunu. eee rund oopparettarmaarudeyum commutator
ithu staanderd vyathiyaanangalude uthppannathin thaazhnna paridhi nalkunnu
canonical commutation bandhatthinte mattoru anantharafalamaanu position momentam oopparettarmaarum parasparam forrier parivarthanangalaanu, athinaal oru vasthuvinte vivaranam athinte momentam anusarichu athinte sthaanathinanusarichu athinte vivaranathinte forrier parivarthanamaanu. forrier vishakalanathil deferentiation duval speysile gunanavumaayi poruthappedunnathinaal, sthaanathe aashrayikkunnathinte forrier parivarthanamaanu momentam oopparettar ennathinartham sthaanathinanusarichu derivative edukkunnathinu (oru formula _ 36 factor vare) thulyamaanu ennaanu. athukondaanu position speysile kwaandam samavakyangalil, momentam formula _ 37-neey formula _ 38 upayogichu maattisthaapikkunnath, prathyekichu position speysile noonn-relativistic shroadinger samavaakyathil momentam-squared padam laplasian times formula _ 39 upayogichu maattisthaapikkunnu.
samyojitha samvidaanangalum ketturappukalum.
rund vyathyastha kwaandam sisttangale orumichu pariganikkumbol, samyojitha sisttathinte hilbert space rund gadakangaludeyum hilbert spaceukal tensor ulppannamaanu. udaaharanathinu, yathaakramam hilbert space formula _ 40, formula _ 41 ennivayulla rund kwaandam systengalaayirikkatte. samyuktha samvidaanathinte hilbert space appol
aadyathe sisttathinte avastha vekttar formula _ 43 umm randaamathe sisttathinte avastha formula _ 44 umm aanenkil, composit sisttathinte avastha
joyint hilbert space formula _ 46 leeii ellah avasthakalum eee roopathil ezhuthaan kazhiyilla, ennirunnaalum, superposition thathwam soochippikkunnathu eee "verthirikkaavunna" allengil "uthppanna avasthakalude" rekheeya samyojanangalum saadhuthayullathaanu ennaanu. udaaharanathinu, formula _ 43 umm formula _ 48 umm sisttam formula _ 32-nuu saadhyamaaya avasthakalaanenkil, athupole formula _ 44 umm formula _ 51 umm sisttam formula _ 33-nuu saadhyamaaya avasthakalaanenkil,
verthirikkaanaavaatha saadhuvaaya samyuktha avasthayaanu. verthirikkaanaavaatha avasthakale entangled ennu vilikkunnu.
oru samyojitha samvidaanathinte avastha ulppettirikkunnuvel, ghadaka samvidaanatheyo samvidaanatheyo oru samsthaana vector vivarikkunnath asaadyamaanu. pakaram, eathenkilum ghadaka samvidaanathil maathram alakkunnathiloode labhikkuna sthithivivarakkanakkukale vivarikkunna kuranja saandrata maatriksukal nirvachikkaan kazhiyum. ithu theerchayaayum vivarangal nashtappedaan kaaranamaakunnu, ennirunnaalum vyakthigatha samvidaanangalude saandrata kurayunna maatriksukal ariyunnathu samyojitha samvidaanathinte avastha punarnirmikkaan paryaapthamalla. saandrata matricks oru valia sisttathinte subsistathinte avastha vyakthamaakkunnathupole, positteev oopparettar-valued alavukal (povms) oru valia sisttathil nadathunna oru alavinte subsistathile phalathe vivarikkunnu. kwaandam vivara sidhaanthathil povmukal vyaapakamaayi upayogikkunnu.
mukalil vivarichathupole, alakkunna prakriyakalude modalukalude oru pradhana savisheshathayaanu entaglent, athil oru upakaranam alakkunna sisttavumaayi entaglent aakunnu. avar thamasikkunna paristhithiyumaayi samvadikkunna samvidaanangal saadhaaranayaayi aaa paristhithiyumaayi kudungikkidakkunnu, ithu kwaandam decoherance ennariyappedunna oru prathibhaasamaan. sookshmadarshanavyavasthayekkal valia samvidaanangalil praayogikamaayi kwaandam efakttukal nireekshikkaan budhimuttunnathu enthukondaanennu ithinu vishadeekarikkaan kazhiyum.
formulationukal thammilulla thulyatha.
kwaandam mekkaaniksinte ganithashaasthraparamaayi thulyamaaya niravadhi formulationukal undu. ettavum pazhakkameriyathum saadhaaranavumaaya onnaanu pooll dirac nirddeshicha "parivartthana sidhaantham", ithu kwaandam mekkaaniksinte rund aadyakaala formulationukale-matricks mechanics (verner heisenberg kandupidichathu), taranga mechanics (ervin shroadinger kandupidichathu) enniva ekeekarikkukayum saamanyavalkkarikkukayum cheiyunnu. kwaandam mekkaaniksinte oru badal roopeekaranam fainmaante paathu integral formulationaanu, athil oru kwaandam-mechanical amplitude prarambha, anthima avasthakalkkidayil saadhyamaaya ellah classical, noonn-classical paathakaludeyum aakethukayaayi kanakkaakkappedunnu. classical mechanicsile aakshan thathwathinte kwaandam-mechanical prathiroopamaanithu.
samamithikalum samrakshana niyamangalum.
hamiltonian formula _ 17 samaya parinaamatthinte "janarettar" ennariyappedunnu, kaaranam ithu formula _ 56-nte oro moolyathinum oru unitory time-evalution oopparettar formula _ 55 nirvachikkunnu. formula _ 57 umm formula _ 17 umm thammilulla eee bandhatthil ninnu, formula _ 17 upayogichu sanjarikkunna eathoru nireekshikkaavunna formula _ 32 umm "samrakshikkappedum": kaalakramena athinte prathekshikkunna moolyam maarilla. eee prasthavana saamaanyavalkkarikkunnu, ganithashaasthraparamaayi, eathoru hermissian oopparettar formulakkum _ 32 nuu oru variable formula _ 56 upayogichu paaraameettar cheytha unitory oopparettarmaarude oru kudumbam srishtikkaan kazhiyum. formula _ 32 upayogichu srishtikkunna parinaamathinu keezhil, formula _ 32 upayogichu sanjarikkunna eathu nireekshikkaavunna formula _ 33 samrakshikkappedum. koodaathe, formula 33-neey formula 32-nuu keezhil parinaamatthiloode samrakshikkukayaanenkil, formula 33-nuu keezhil srishtikkappetta parinaamathinu keezhil formula 32 samrakshikkappedunnu. ithu classical (lagranchian) mechanicsil emmy nother theliyikkunna phalatthinte oru kwaandam pathippine soochippikkunnu oru haamilttaniyante oro deferentiable samamitikkum, anubandha samrakshana niyamam nilavilundu.
udaaharanagal.
swatantra kanika.
position digri oof freedam ulla oru kwaandam sisttathinte ettavum lalithamaaya udaaharanam orotta speshyal alavilulla oru swatantra kanikayanu. oru swatantra kanika ennathu baahya swaadheenangalkku vidheyamallaatha onnaanu, athinaal athinte hamiltonian athinte gathikorjjam maathram ulkkollunnu
shroadinger samavaakyathinte pothuvaaya pariharam nalkunnathu
ithu saadhyamaaya ellah playin tharamgangalude formulayude superpositionaanu, avaa momentam formula _ 73 ulla momentam oopparettarude eejanstettukalaanu. superpositionte gunakangal formula _ 74 aanu, ithu prarambha kwaandam stettu formula _ 75 nte forrier parivarthanamaanu.
iva saadhaarana nilavaaramulla kwaandam avasthakalallaathathinaal pariharam orotta momentam eejanstettu allengil orotta position eejanstettu aakaan kazhiyilla. pakaram, namukk oru gausiyan taranga paakkat pariganikkaam
ithinu forrier parivarthanamundu, athinaal momentam vitharanam
formula _ 78 cheruthaakkumbol sthaanathe spread cheruthaanenkilum momentatthile spread valuthaakkunnuvenn nammal kaanunnu. neremarichu, formula _ 78 valuthaakkunnathiloode nammal vegathayil spread cheruthaakkunnu, pakshe sthaanathe spread valuthaakkunnu. ithu anishchithathva thathwathe vyakthamaakkunnu.
gossian taranga paakkat kaalakramena vikasikkaan anuvadikkumbol, athinte kendram sthiramaaya vegathayil bahiraakaashatthiloode neengunnathu nammal kaanunnu (athil pravartthikkunna shakthikalillaatha oru classical kanika pole). ennirunnaalum, samayam purogamikkumbol taranga pakkattum vyapikkum, athaayath sthaanam kooduthal kooduthal anishchithathvathilaakunnu. ennirunnaalum, vegathayile anishchithathvam sthiramaayi thudarunnu.
oru pettiyile kanika.
ekamaana pottensial energy boxile kanika ganithashaasthraparamaayi ettavum lalithamaaya udaaharanamaanu, avide niyanthranangal oorjja nilakalude alavu nischayikkunnathilekku nayikkunnu. oru prathyeka pradeshathinullil ellaayidathum poojyamaaya pottensial oorjjam ullathinaal aaa pradeshathinu purathu ellaayidathum ananthamaaya pottensial oorjjam ullathayi boxes nirvachikkappedunnu. formula _ 80 dishayilulla ekamaana kesil, samaya-swatantra shroadinger samavaakyam ezhuthaam.
nirvachicha deferential oopparettar
munbathe samavaakyam classic kainettik energy analoginte aavirbhaavamaanu,
eee saahacharyathil oorjja soothravaakyam ulla avastha soothravaakyam _ 1 kanikayude gathikorjavumaayi poruthappedunnu.
oru boxile kanikaykkulla shroadinger samavaakyathinte pothuvaaya pariharangal ivayaanu
allengil, yoolarude soothravaakyathil ninnu,
boxinte ananthamaaya pottensial mathilukal formula _ 88, formula _ 89 ennivayude moolyangal formula _ 90, formula _ 91 ennivayil nirnnayikkunnu, avide formula _ 1 poojyamaayirikkanam. athinaal, formula _ 90 ll,
formula 95. formula 91 ll,
eathu formula _ 98 poojyamaakaan kazhiyilla, kaaranam ithu formula _ 1 nuu maanadandam 1 ullathinaal, formula _ 100 aayathinal, formula _ 101 formula _ 102 nte oru poornnasankhya gunithamayirikkanam,
formula _ 89-leeii eee niyanthranam oorjja nilavaaratthil oru parimitiye soochippikkunnu, vilavu
soothravaakyam _ 105
parimithamaaya aazhamulla saadhyathayulla kinarukalilekkulla ananthamaaya saadhyathayulla kinarinte prashnatthinte saamaanyavalkkaranamaanu parimithamaaya saadhyathayulla kinner. kinarinte chuvarukalil tharamgapravartthanam poojyathilekku pinn cheyyaathathinaal parimithamaaya pottensial kinner prashnam ananthamaaya kanika-inn-eiii-boxes prashnathekkaal ganithashaasthraparamaayi kooduthal sankeernamaanu. pakaram, kinarinu purathulla pradeshangalil poojyamallaathathinaal tharamgapravartthanam kooduthal sankeernamaaya ganitha athirthi vyavasthakal thripthippeduthanam. flash memory, scanning tunneling microscopy thudangiya aadhunika saankethikavidyakalude prakadanatthil pradhana punk vahikkunna kwaandam tunneling efakttinaayi oru maathruka nalkunna chathuraakrithiyilulla pottensial barrieranu mattoru anubandha prashnam.
harmonic oosilettar.
classical kesil ennapole, kwaandam harmonic oosilettarinte pottensial nalkunnathu
nissaaramallaattha shroadinger samavaakyam nerittu pariharikkunnathiloodeyo pooll dirac aadyam nirddeshicha kooduthal gambheeramaaya "ladder reethi" upayogicho eee prashnam pariharikkanaakum. aijanstettukal nalkunnathu
hermite polynomialukal evideyaanu "echen
anubandha oorjja nilakal ivayaanu
bandhithaavasthakalkkulla oorjjathinte vivechanam vyakthamaakkunna mattoru udaaharanamaanithu.
mack-sender interferometer.
mack-sender interferometer (emm. sii. aii) deferential samavaakyangalekkaal alavu 2 ll leanier aaljibrayumaayi superposition, edapedal ennivayude ashayangal chithreekarikkunnu. eratta-slitt pareekshanatthinte lalithamaaya pathippayi ithine kaanaan kazhiyum, pakshe ithu athintethaaya thaalpparyamullathaanu, udaaharanathinu kaalathamasam varuthiya kwaandam iresar, elitsar-wideman bomb testtar, kwaandam entaamgilment padanangal ennivayil.
interferometeriloode kadannupokunna oru phottoon oro ghattathilum rund paathakalude superpositionil maathramaayirikkumenn pariganichukondu namukk maathrkayaakkaan kazhiyum idathuninnu aarambhich rund beam splittarukaliloodeyum nere pooyi mukalil avasaanikkunna "lover" paathu, thaazhe ninnu aarambikkunna "upper" paathu, rund beam splittarukaliloodeyum nere pooyi valathuvashath avasaanikkunnu. athinaal photoninte kwaandam avastha oru vekttar formulayanu-111, athu "lover" paathu formula _ 112-nteyum "upper" paathu formula _ 113-nteyum superpositionaanu, athaayath, sankeernamaaya formula _ 115-nuu formula _ 114. aaa formula _ 116-neey maanikkunnathin namukk aaa formula _ 117 aavasyamaanu.
rund beam splittarukalum unitory matricks formula _ 118 aayi maathrkayaakkunnu, athaayath oru phottoon beam splittarumaayi koodikkaazhcha nadathumbol athu onnukil formula _ 119 nte probability aamplityoodumaayi ore pathayil thudarum, allengil formula _ 120 nte probability aamplityoodumaayi mattoru paathayilekku prathifalikkum. mukalile kaiyile phase shifttar unitory matricks formula _ 121 aayi maathrkayaakkiyirikkunnu, athaayath phottoon "mukalile" paathayilaanengil athu formula _ 122 nte aapekshika ghattam nedum, athu thaazhathe paathayilaanengil athu maattamillathe thudarum.
idathuninnu interferometerilekku praveshikkunna oru phottoon pinneedu oru beam splittar formula _ 33, oru phase shifttar formula _ 28, mattoru beam splittar formula _ 33 enniva upayogichu pravartthikkukayum angane avasthayil avasaanikkukayum cheyyum. 
ithu valathuvashatho mukaliloo kandethanulla saadhyathakal yathaakramam nalkunnu
athinaal eee saadhyathakal kanakkakkikkondu ghattam maattam kanakkakkaan oraalkk mack-sender interferometer upayogikkaam.
phottoon theerchayaayum beam splittarukalkkidayila "thaazhathe" allengil "mukalile" paathakalilaanenkil enthu sambhavikkumennu pariganikkunnath rasakaramaan. oru paatha thadayunnathiloodeyo allengil aadyathe beam splittar neekkam cheiyunnathiloodeyo (aavashyamullathupole idathuninnu allengil thaazhe ninnu photoninu bhakshanam nalkunnathiloodeyo) ithu saadhyamaakkaam. rund saahacharyangalilum inii paathakalkkidayil oru thadassavum undaakilla, koodaathe phase formula _ 122 ll ninnu swathanthramaayi formula _ 129 vazhiyaan saadhyathakal nalkunnathu. ithil ninnu namukk nigamanam cheyyaan kazhiyum, phottoon aadyathe beam splittarin sesham onno allengil mattoo paatha edukkunnilla, marichu athu rund paathakaludeyum yadhaartha kwaandam superpositionilaanennu.
aaplikkeshanukal.
classical reethikalaal vishadeekarikkaan kazhiyaatha cheruthum vyathirikthavumaya alavukalum edapedalukalum sambandhichu nammude prapanchatthinte pala savisheshathakalum vishadeekarikkunnathil kwaandam mechanics valia vijayam nediyittundu. ellah tharatthilulla dravyangalum (electronukal, protonukal, neutronukal, photonukal, mattullava) ulkkollunna upa aattomik kanangalude vyakthigatha perumattangal velippeduthaan kazhiyunna oreyoru sidhaanthamaanu kwaandam mechanics. soolid-stettu physix meteeriyals science kwaandam mechanicsine aasrayichirikkunnu.
pala kaaryangalilum aadhunika saankethikavidya pravartthikkunnathu kwaandam efakttukal praadhaanyamarhikkunna alavilaanu. kwaandam kemistry, kwaandam optiks, kwaandam computing, superconducting magnettukal, laitt emitting diodeukal, opttikkal amplifier, lazer, traansisttar, microprosessor polulla ardhachaalakangal, magnetic resonance imaging, electron microscopy thudangiya medical, gaveshana imaging enniva kwaandam sidhaanthathinte pradhana prayogangalil ulppedunnu. niravadhi jaiva, bhauthika prathibhaasangalude vishadeekaranangal raasabandhathinte swabhaavathil veroonniyathaanu, prathyekichu macro-molecule dna.
mattu shaasthreeya sidhaanthangalumaayi bandhappettirikkunnu.
classical mechanics.
kwaandam mekkaaniksinte niyamangal oru sisttathinte stettu space oru hilbert space aanennum sisttathinte nireekshanangal aaa sthalathe vektarukalil pravartthikkunna hermissian oopparettarmaaraanennum vaadikkunnu-ennirunnaalum eathu hilbert space allengil eathu oopparettarmaaraanennu avar nammodu parayunnilla. bhauthika pravachanangal nadathunnathinulla aavashyamaaya gattamaaya oru kwaandam sisttathinte alavilulla vivaranam labhikkunnathin iva uchithamayi thiranjedukkaam. eee thiranjeduppukal nadathunnathinulla oru pradhana maarganirddeshamaanu correspondence thathwam, kwaandam mekkaaniksinte pravachanangal valia kwaandam samkhyakalude bharanathil classical mekkaaniksinte pravachanangalilekku kurayunnuvennu parayunna oru huristic. oru prathyeka samvidaanathinte sthaapithamaaya classical modalil ninnu aarambhikkaanum thudarnnu correspondence paridhiyil classical modalinu kaaranamakunna adisthaana kwaandam model oohikkaanum sramikkaam. eee sameepanathe quandisation ennu vilikkunnu.
kwaandam mechanics yadhaarthathil roopappeduthiyappol, parasparabandhithamallaatha classical mechanics enna kathidapaadukalude paridhi ulla modalukalil ithu prayogichu. udaaharanathinu, kwaandam harmonic oosilettarinte ariyappedunna model oosilettarinte gathikorjjathinaayi vyakthamaayi noonn-relativistic expression upayogikkunnu, athinaal ithu classical harmonic oosilettarinte oru kwaandam pathippaanu.
nalla kwaandam nambarukalillaattha araajakathva samvidaanangalil sankeernathakal undaakukayum eee samvidaanangalile classical, kwaandam vivaranagal thammilulla bandham kwaandam araajakathvam padikkukayum cheiyunnu.
kwaandam systengalkku yojip nashtappedukayum angane niravadhi saadhaarana kwaandam efakttukal pradarshippikkaan kazhiyaathe varikayum cheiyunna oru samvidaanamaanu kwaandam decoherensa kwaandam superpositionukal kevalam probabilistik misrithangalaayi maarunnu, koodaathe kwaandam entaamgilment classical paraspara bandhangalayi maarunnu. kwaandam swabhaavam macroscopic aayi prakadamaayekkaavunna kevala poojyathilekku adukkunna thaapanilayilozhike macroscopic skeyilukalil kwaandam yojip saadhaaranayaayi prakadamalla.
oru classical sisttathinte niravadhi macroscopic gunangal athinte bhaagangalude kwaandam swabhaavathinte nerittulla anantharafalamaanu. udaaharanathinu, bulk dravyathinte sthiratha (vaidyuthashakthikalkku keezhil maathram vegathil takarunna aattangalum thanmaathrakalum ulkkollunnu), kharapadaarthangalude kaadinyam, dravyathinte mechanical, thermal, kemikkal, opttikkal, magnetic propertykal ennivayellaam kwaandam mekkaaniksinte niyamangalkk keezhilulla vaidyutha chaarjukalude prathipravartthanatthinte falamaanu.
special relativityum electrodynamics.
kwaandam mechanicsine prathyeka aapekshikathayumayi layippikkanulla aadyakaala sramangalil shroadinger samavaakyathe clain-gorden samavaakyam allengil diarac samavaakyam polulla oru koveriyant samavaakyam upayogichu maattisthaapikkuka ulppedunnu. eee sidhaanthangal niravadhi pareekshanathmaka phalangal vishadeekarikkunnathil vijayichenkilum, aapekshika srishtiyeyum kanangalude naashatheyum avaganayil ninnu uthbhavikkunna chila thripthikaramallaatha gunangal avaykku undaayirunnu. oru poornnamaaya aapekshika kwaandam sidhaanthathinu kwaandam feeld sidhaanthathinte vikasanam aavasyamaanu, ithu oru feeldil (oru nischitha kanangalude koottatthinupakaram) quandisation prayogikkunnu. aadyathe samboornna kwaandam feeld sidhaanthamaaya kwaandam electrodynamics, vaidyuthakaanthika edapedalinekkurichu poornnamaaya kwaandam vivaranam nalkunnu. kwaandam electrodynamics, pothu aapekshikathaykkoppam, ithuvare aavishkarichathil vachu ettavum krithyamaaya bhauthika sidhaanthangalilonnaanu.
electrodynamic samvidaanangale vivarikkunnathin kwaandam feeld sidhaanthathinte poornna upakaranam palappozhum anaavasyamaanu. kwaandam mekkaaniksinte thudakkam muthal upayogichirunna oru lalithamaaya sameepanam, charjju cheytha kanangale oru classical vaidyuthakaanthikakshethram pravartthikkunna kwaandam mechanical vasthukkalaayi kanakkaakkuka ennathaanu. udaaharanathinu, hydrajan aattathinte praadhamika kwaandam model oru classical soothravaakyam _ 131 coolumb pottensial upayogichu hydrajan aattathinte vaidyutha mandalathe vivarikkunnu. vaidyuthakaanthika mandalatthile kwaandam ettakkurachilukal charjju cheytha kanikakalaal photonukalude puranthallal polulla oru pradhana punk vahikkukayaanenkil eee "semi-classical" sameepanam paraajayappedunnu.
sakthamaaya aanavashakthikkum durbalamaaya aanavashakthikkum vendiyulla kwaandam feeld sidhaanthangalum vikasippichittund. sakthamaaya nuclear fozhsinte kwaandam feeld sidhaanthathe kwaandam chromodynamics ennu vilikkunnu, ithu kwaarkkukal, gluvonukal thudangiya subnuclear kanangalude edapedalukale vivarikkunnu. durbalamaaya aanavashakthiyum vaidyuthakaanthikashakthiyum avayude alavu roopangalil bhauthikashaasthranjaraaya abdus salaam, sheldon glasho, steevan weinberg ennivar chernnu orotta kwaandam feeld sidhaanthamaayi (electrovic sidhaantham ennariyappedunnu) samyojippichu.
pothuvaaya aapekshikathayumayulla bandham.
kwaandam sidhaanthathinteyum pothuvaaya aapekshikathayudeyum pravachanangale karsanavum aavarthichullathumaya anubhavaparamaya thelivukal pinthunaykkunnundena, avayude amoorthamaaya aupachaarikathakal parasparam vairudhyamullavayaanennum avaa sthirathayullathum yojichathumaaya oru maathrkayil ulppeduthunnathu valare budhimuttaanennum theliyikkappettittund. kanika bhauthikashaasthrathinte pala mekhalakalilum guruthwaakarshanam valare kuravaanu, athinaal pothu aapekshikathayum kwaandam mechanics thammilulla ekeekaranam aaa prathyeka prayogangalil adiyanthira prashnamalla. ennirunnaalum, kwaandam guruthwaakarshanathinte sariyaaya sidhaanthathinte abhavam bhauthika prapanchashaasthrathilum bhouthikashaasthranjarude oru gambheeramaaya "ellaattinteyum sidhaantham" (calviral) enna anweshanathilum oru pradhana prasnamaanu. thalphalamaayi, rund sidhaanthangalum thammilulla poruthakkedukal pariharikkuka ennathu 20-aamm noottaandileyum 21-aamm noottaandileyum bhauthikashaasthrathinte oru pradhana lakshyamaanu. eee calviral upaparamaanavashasthrathinte maathrkakale samyojippikkuka mathramalla, orotta shakthiyil ninno prathibhaasatthil ninno prakrithiyude naalu adisthaana sakthikal nedukayum cheyyum.
angane cheiyunnathinulla oru nirddesham string sidhaanthamaanu, ithu kanika bhauthikashaasthrathile pooyint polulla kanikakalkku pakaram strings ennariyappedunna oru dimensional objectukal sthaapikkunnu. eee stringukal engane bahiraakaashatthiloode pracharippikkukayum parasparam edapedukayum cheiyunnuvennu string sidhaantham vivarikkunnu. string skeyilinekkaal valia dhoora skeyilukalil, oru string oru saadhaarana kanika pole kaanapedunnu, athinte pindam, charge, mattu gunangal enniva stringinte vibrational avastha nirnnayikkunnu. string sidhaanthathil, stringinte niravadhi vibrational avasthakalilonnu guruthwaakarshana shakti vahikkunna kwaandam mechanical kanikayaaya graavittanumaayi poruthappedunnu.
mattoru janapriya sidhaantham lupe kwaandam guruthwaakarshanamaanu (ell. kyu. jii), ithu guruthwaakarshanathinte kwaandam gunangale vivarikkunnu, athinaal ithu kwaandam space taiminte sidhaanthamaanu. staanderd kwaandam mechanics staanderd general relativityum layippikkanum poruthappeduthaanumalla sramamaanu ell. kyu. jii. spin netvarkkukal ennu vilikkunna parimithamaaya looppukalude "neytha" valare mikacha thuniyaanu eee sidhaantham bahiraakaashathe visheshippikkunnathu. kaalakramena oru spin netvarkkinte parinaamatthe spin phoom ennu vilikkunnu. oru spin fomte swabhaava dairkhya skeyil plank neelamaanu, ekadesham 1.616 × 10−35 meter, athinaal plank neelathekkaal cheria neelangal lqg-ll bhouthikamaayi ardhamaakkunnilla.
daarshanika prathyaaghaathangal.
athinte thudakkam muthal, kwaandam mekkaaniksinte niravadhi ethir-avabodhajanya vashangalum phalangalum sakthamaaya daarshanika samvaadangalkkum niravadhi vyaakhyaanangalkkum kaaranamaayittund. kwaandam mekkaaniksinte probabilistik swabhaavam, tharamgapravartthana thakarchayileyum anubandha alaveduppu prashnathileyum budhimuttukal, kwaandam nonlokkaality ennivaye kendreekarichaanu vaadangal. orupakshe eee vishayangalil nilanilkkunna eaka samavayam samavaayamilla ennathaanu. richard fainman orikkal paranju, "kwaandam mechanics arcum manassilaakillenn enikku surakshithamaayi parayaan kazhiyumennu njaan karuthunnu."steevan weinberginte abhipraayathil", kwaandam mekkaaniksinte poornnamaayum thripthikaramaaya vyaakhyaanamonnum ippol ente abhipraayathil illa."
neels booar, verner heisenberg, mattu bhauthikashaasthranjar ennivarude kaazhchappaadukal palappozhum "copenhagen vyaakhyaanam" aayi tharamthirickunnu. eee kaazhchappaadukal anusarichu, kwaandam mekkaaniksinte probabilistik swabhaavam oru "thaalkkaalika" savisheshathayalla, athu oduvil oru nirnnayaka sidhaantham upayogichu maattisthaapikkappedum, pakaram "kaaryakaarana" enna classical aashayathinte "anthima" thyagamaanu. vyathyastha pareekshanathmaka saahacharyangalil labhicha thelivukalude pooraka swabhaavam kaaranam, kwaandam mechanical aupachaarikathayude nannayi nirvachikkapetta eathoru prayogavum ellaayppozhum pareekshanathmaka krameekaranatthe paraamarshikkanamenn booar prathyekichum oonnipparanju. 21-aamm noottaandil copenhagen tharatthilulla vyaakhyaanangal janapriyamaayi thudarunnu.
kwaandam sidhaanthathinte sthaapakariloraalaaya albert ainsteen, nirnnayavaadavum pradeshavum polulla chila vilamathikkappedunna metaafisikkal thathwangale maanikkunnathil parajayappettathil aswasthanaayirunnu. kwaandam mekkaaniksinte ardhatheyum avasthayeyum kurichu borumaayulla ainsteente deerghakaala kaimattangal ippol booar-ainsteen samvaadangal ennariyappedunnu. adisthaanaparamaaya kwaandam mechanics akaleyulla pravartthanatthe vyakthamaayi nirodhikkunna oru sidhaanthamaayirikkanam ennu ainsteen vishwasichu. kwaandam mechanics apoornnamaanennum, saadhuthayullathum ennaal adisthaanaparamallaathathumaya oru sidhaantham, thermodynamics engane saadhuthayullathaanennu addeham vaadichu, ennaal athinte pinnile adisthaana sidhaantham stattistikkal mechanicsaanu. 1935-ll ainsteenum addehathinte sahakarikalaaya boris podolsky nathan rosen chernnu pradeshatthinte thathwam kwaandam mekkaaniksinte apoornnathaye soochippikkunnuvennu oru vaadam prasidheekarichu, eee chinta pareekshanatthe pinneedu ainsteen-podolsky-rosen paradox ennu vilichu. 1964-ll, eiii. pii. aarinte praadeshikathayude thathwam, nirnnayavaadathodoppam, yadhaarthathil kwaandam mechanicsumaayi poruthappedunnillenna joonn bell kaanichu avar vidoora samvidaanangal ulppaadippikkunna parasparabandhangalil parimithikal soochippikkunnu, ippol bell asamathvangal ennariyappedunnu, avaa kettiya kanikakalaal lamghikkappedaam. athinusesham eee parasparabandhangal nedunnathinaayi niravadhi pareekshanangal nadathiyittundu, athinte falamaayi avaa yadhaarthathil bell asamathvangal lamghikkukayum angane nirnnayavaadavumaayulla pradeshatthinte samyojanathe thettayi chithreekarikkukayum cheiyunnu.
kwaandam mechanicsine vyakthamaayi nonlokkal akkunna vilaykk nirnnaayakamaakkunnathin athu parishkarikkaan kazhiyumennu bohmian mechanics kaanikkunnu. ithu oru bhauthika samvidaanathinu oru tharamgapravartthanathe mathramalla, koodaathe oru praadeshikamallaatha maarganirddesha samavaakyathin keezhil nirnnaayakamaayi parinamikkunna oru yadhaartha sthaanatheyum attribute cheiyunnu. oru bhauthika samvidaanathinte parinamam ellaayppozhum nalkunnathu maarganirddesha samavaakyathodoppam shroadinger samavaakyamaan; tharamgapravartthanathinte thakarcha orikkalum undaakilla. ithu alaveduppinte prashnam pariharikkunnu.
1956ll roopappeduthiya evarattinte bahu-loka vyaakhyaanathil, "kwaandam sidhaantham vivarikkunna ellah saadhyathakalum" oresamayam kooduthalum swatantra samanthara prapanchangal chernna oru malttivezhsilaanu sambhavikkunnath ennu parayunnu. taranga paakkattinte thakarchayude soothravaakyam neekkam cheythathinte anantharafalamaanithu. alakkunna samvidaanathinteyum alakkunna upakaranathinteyum saadhyamaaya ellah avasthakalum nireekshakanodoppam oru yadhaartha bhauthika kwaandam superpositionil undu. malttivezhs nirnnaayakamaanenkilum, saadhyathakalaal niyanthrikkappedunna nirnnaayakamallaatha perumaattam njangal manassilakkunnu, kaaranam njangal malttivezhsine mothatthil nireekshikkunnilla, marichu oru samayat oru samanthara prapancham maathrame nireekshikkunnulloo. ithu engane pravarthikkumennathu valare charchaavishayamaanu. ithu manassilakkaanum avaa vijayakaramaano ennathinekkurichu samavaayamillathe janmana niyamam nedaanum niravadhi sramangal nadathiyittundu.
1990 kalude avasaanathil relational kwaandam mechanics copenhagen-tharam aashayangalude aadhunika derivateevaayi prathyakshappettu, kurachu varshangalkk sesham cubism vikasippichu.
charithram.
20-aamm noottaandinte aadya dashakangalil kwaandam mechanics vikasippicheduthu, chila sandarbhangalil, munkaalangalil nireekshikkappetta prathibhasangal vishadeekarikkendathinte aavasyakathayaanu ithu. roobert hook, kristhyan hyujans, leonhard euler thudangiya shaasthranjar pareekshanathmaka nireekshanangale adisthaanamaakki prakaashatthinte taranga sidhaantham nirddeshichappol 17,18 noottaandukalil prakaashatthinte taranga swabhaavathekkurichulla shaasthreeya anweshanam aarambhichu. 1803ll engleesh polimathu thomas yang prashasthamaaya double slitt pareekshanatthe vivarichu. prakaashatthinte taranga sidhaanthathinte pothuvaaya sveekaaryathayil eee pareekshanam oru pradhana punk vahichu.
pathonpathaam noottaandinte thudakkathil, joonn daltonteyum amedio avagadroyudeyum raasa gaveshanam dravyathinte aattomik sidhaanthathinu praadhaanyam nalki, jaims clark maiks well, ludwig boltsman, mattullavar ennivar vaathakangalude gathiko sidhaantham sthaapikkunnathinaayi nirmmicha oru aashayamaanith. chalanathmaka sidhaanthathinte vijayangal dravyam aattangalaal nirmmithamaanenna aashayathin kooduthal vishwaasyatha nalki, ennittum sidhaanthathinu kuravukalum undaayirunnu, athu kwaandam mekkaaniksinte vikasanathiloode maathrame pariharikkaanaakoo. greak thathwachinthayil ninnulla aattangalekkurichulla aadyakaala sangalppangal avaa avibhaajya unitukalaanennu aayirunnuvenkilum pathonpathaam noottaandil "aattam" enna vaakk "uncutable" ennartham varunna greekkil ninnu uruthirinjathaanu. 1838ll maikkal farreday nadatthiya oru nireekshanam thaazhnna marddathil vaathakam adangiya oru glass tubinullile vaidyutha visarjanam moolamundaakunna thilakkathekkurichulla oru pradhana kandethalaayirunnu. juuliyas plucker, johann wilhem hittorf, yoojan goldstein ennivar faaradeyude pravartthanangal thudarukayum mechappeduthukayum cheythu, ithu cathode kiranangal thirichariyunnathilekku nayichu, ithu jeey. jeey. electronukal ennu vilikkappedunna upa aattomik kanikakal adangiyirikkunnuvennu thomson kandethi.
1859-ll gustav kirchoff aanu black body radiation prashnam kandethiyathu. 1900-ll, maiks plank oorjjam vikiranam cheyyappedukayum vyathirikthamaya "kwanda" (allengil oorjja paakkattukal) ll agiranam cheyyappedukayum cheiyunnuvenna sidhaantham nirddeshichu, ithu black body radiationte nireekshicha paattenukalumaayi krithyamaayi poruthappedunna oru kanakkukoottal nalkunnu. ethra valuth" allengil "ethra" ennartham varunna laattin padatthil ninnaan "kwaandam" enna vaakk uruthirinjathu. plank anusarichu, oorjjathinte alavukale avayude valuppam ("iii") avayude aavruthikku ("ν") aanupaathikamaaya "moolakangal" aayi vibhajikkunnathayi kanakkakkaam
ivide "h" ennathu plaankinte sthiraankamaanu. ithu vikiranathinte agiranam, udvamanam ennivayude prakriyakalude oru vasham maathramaanennum vikiranathinte "bhauthika yaadhaarthyam" allennum plank jaagrathayode vaadichu. vaasthavathil, thante kwaandam sidhaanthathe addeham oru valia kandethalinekkaal sariyaaya utharam nedunnathinulla ganithashaasthra thanthramaayi kanakkakki. ennirunnaalum, 1905-ll albert ainsteen plaankinte kwaandam sidhaanthathe yaadhaarthyabodhathode vyaakhyaanikkukayum foto electric ephakt vishadeekarikkaan ithu upayogikkukayum cheythu, athil chila vasthukkalude prakashikkunna prakaashathinu padaarthatthil ninnu electronukal puranthallaan kazhiyum. hydrajante spectral lineukal vijayakaramaayi pravachicha hydrajan aattathinte oru maathrkayaayi vikiranathekkurichulla plaankinte ashayangal neels booar vikasippichu. prakasham polulla oru vaidyuthakaanthika tharamgathe athinte aavruthiye aashrayich vyathirikthamaya oorjjamulla oru kanika (pinneedu phottoon ennu vilikkapettu) ennum visheshippikkaamennu kaanikkunnathinaayi ainsteen eee ashayam vikasippichu. oonn dhii kwaandam thiyari oof radiation" enna thante prabandhatthil, aattangalude oorjjathinte agiranam, puranthallal enniva vishadeekarikkunnathinaayi oorjjavum dravyavum thammilulla prathipravartthanathekkur ainsteen vishadeekarichu. addehathinte pothuvaaya aapekshikatha sidhaantham akkaalat maranjirunnuvenkilum, eee prabandham vikiranathinte uthejippicha udvamanathinu adisthaanamaaya samvidaanathe vyakthamaakkukayum athu laserinte adisthaanamaayi maarukayum cheythu.
eee ghattathe pazhaya kwaandam sidhaantham ennu vilikkunnu. orikkalum poornnamo svayam sthirathayullatho aayirunnilla, pazhaya kwaandam sidhaantham classical mekkaniksilekkulla huristic thiruthalukalude oru koottamaayirunnu. aadhunika kwaandam mekkaaniksinte ardha-classical ekadesha kanakkayi eee sidhaantham ippol manassilaakkappedunnu. eee kaalaghattatthile sradheyamaaya phalangalil, mukalil soochippicha plank, ainsteen, booar ennivarude pravarthanangalkku purame, kharapadaarthangalude nirddishta thaapathekkurichulla ainsteenteyum peettar debyudeyum pravartthanangal, classical physixine diamagnettisathinu kaaranamaakillenn booar, hendrica johanna vaan luvan ennivarude thelivukal, prathyeka aapekshika phalangal ulppeduthunnathinaayi arnold somerfeld booar modalinte vipuleekaranam enniva ulppedunnu.
1920kalude madhyathil aattomik physixinte staanderd formulationaayi kwaandam mechanics vikasippichu. 1923-ll franch bhauthikashaasthranjanaaya luis dii brogley thante dravyatharamgangalude sidhaantham munnottuvachu, kanangalkk taranga savisheshathakal prakadippikkaan kazhiyumennu prasthaavichu. dii brogliyude sameepanathe adisthaanamaakki, 1925-ll jarmman bhauthikashaasthranjaraaya verner heisenberg, maiks boonn, pascuval jordan ennivar matricks mechanics vikasippikkukayum austriyan bhauthikashaasthranjanaaya ervin shroadinger taranga mechanics kandupidikkukayum cheythappozhaanu aadhunika kwaandam mechanics janichathu. 1926 joolaiyil shrodingerude tharamgapravartthanathinte saadhyataa vyaakhyaanam boonn avatharippichu. angane, kwaandam physixinte muzhuvan mekhalayum uyarnnuvannu, ithu 1927 leeii anchaam solway konfaransil athinte vishalamaaya sveekaaryathayilekku nayichu.
1930 aayappozhekkum david hilbert, pooll dirac, joonn voonn neuman ennivar alakkal, yaadhaarthyathekkurichu nammude arivinte stattistikkal swabhaavam, 'nireekshakane'kkurichulla daarshanika oohaapohangal ennivaykku kooduthal oonnal nalkikkond kwaandam mechanics kooduthal ekeekrithavum aupachaarikavalkkarikkappedum cheythu. athinusesham ithu kwaandam kemistry, kwaandam electronics, kwaandam optiks, kwaandam information sayans ennivayulppede niravadhi vishayangalil vyaapikkukayum cheythu. aadhunika periodic table oof elamentukalude niravadhi savisheshathakalkk ithu oru upayogapradamaaya chattakoodum nalkunnu, koodaathe raasabandhathinidayilulla aattangalude perumattangalum computer ardhachaalakangalile electronukalude ozhukkum vivarikkunnu, athinaal pala aadhunika saankethikavidyakalilum ithu nirnaayaka punk vahikkunnu. valare cheria lokathe vivarikkaanaan kwaandam mechanics nirmmikkappettathenkilum, soopparkandaktarukal, superfluidukal thudangiya chila macroscopic prathibhaasangalum vishadeekarikkendathundu.
kooduthal vaayana.
thaazhepparayunna thalakkettukal, jolie cheiyunna bhauthikashaasthranjar, kuranjathu saankethika upakaranangal upayogichu saadhaaranakkaarumaayi kwaandam sidhaantham ashayavinimayam nadatthaan shramikkunnu.
kooduthal saankethikavidya
vikkibukkukalil

