
mikacha ghadana

aattomik physixil, electron spin moolamulla aattangalude spectral lainukalude vibhajanavum noonn-relativistic shroadinger samavaakyathilekkulla relativistic thiruthalukalum phine structure vivarikkunnu. hydrajan aattathin krithyamaayi alannathu albert eiii aanu. michaelson edward dablyu. 1887-ll morley, arnold somerfeldinte saidhaanthika chikilsaykku adithara paakukayum phine-structure sthiraangam avatharippikkukayum cheythu.
pashchaathalam.
motha ghadana.
line spectrayude "motha ghadana" ennathu karakkamillaatha noonn-relativistic electronukalude kwaandam mechanics pravachikkunna line spectrayaanu. oru hydragenic aattathe sambandhichidatholam, motham ghadana oorjja nilakal pradhana kwaandam nambaraaya "n" neey maathram aasrayichirikkunnu. ennirunnaalum, kooduthal krithyamaaya oru maathruka aapekshikavum karangunnathumaya phalangal kanakkiledukkunnu, ithu oorjja nilakalude apachayathe thakarkkukayum spectral lainukale vibhajikkukayum cheiyunnu. motha ghadana oorjjavumaayi thaarathamyappeduthumbol phine structure vibhajanathinte skeyil ("zα") 2 enna kramathilaanu, ivide "z" ennathu aattomik number "α" phine structure sthiraankavumaanu, ekadesham 1/137 nuu thulyamaaya alavillaatha samkhya.
aapekshikamaya thiruthalukal.
perterbation sidhaantham upayogichu phine structure energy thiruthalukal nedaanaakum. eee kanakkukoottal nadatthaan oraal hamiltonian enna moonnu thiruthal padangal cherkkanam gathikorjjathilekkulla leading oordar relativistic thiruthal, spin-oorbitt coupling moolamulla thiruthal, electroninte kwaandam ettakkurachilukalil ninnu varunna darvin padam allengil sitterbegang.
dairaakkinte sidhaantham swaabhaavikamaayi aapekshikathayum spin edapedalukalum ulkkollunnathinaal diarac samavaakyathinte aapekshikathayallaatha paridhiyil ninnum eee thiruthalukal nedaanaakum.
hydrajan aattam.
eee vibhaagam hydrajan aattathinte vishakalana pariharangal charcha cheiyunnu, kaaranam prashnam vishakalanaparamayi pariharikkavunnathum kooduthal sankeernamaaya aattangalile oorjja nila kanakkukoottalukalude adisthaana maathrkayumaanu.
gathikorja aapekshika thiruthal.
motha ghadana haamiltoniyante gathikorja padam classical mechanicsil ulla athe roopamedukkunnuvennu anumaanikkunnu, ithu orotta electroninu ardhamaakkunnu.
soothravaakyam _ 1
pottensial energy evideyaanu, formula _ 2 ennathu momentam, formula _ 3 ennathu electron restt maas aanu.
ennirunnaalum, prathyeka aapekshikathayiloode prakrithiyekkurichulla kooduthal krithyamaaya oru sidhaantham pariganikkumbol, chalanathmaka oorjjathinte aapekshika roopam naam upayogikkanam.
formula _ 4
ivide aadya padam motham aapekshika oorjjavum randaamathe padam electroninte backie oorjjavumaanu (soothravaakyam _ 5 prakaashatthinte vegathayaanu). formula _ 5-nte valia moolyangalkkaayi square root vipuleekarikkunnathaayi nammal kandethunnu.
soothravaakyam _ 7
eee shreniyil ananthamaaya ennam padangalundenkilum, pinneedulla padangal munbathe padangale apekshichu valare cheruthaanu, athinaal aadyathe randozhike matellaam namukk avaganikkaam. mukalilulla aadya padam ithinakam classical hamiltoniante bhagamaayathinaal, hamiltonian ennathinu aadya kramam "thiruthal" aanu
soothravaakyam _ 8
ithu oru aswasthathayaayi upayogichu, aapekshika phalangal moolamulla aadya oordar oorjja thiruthalukal namukk kanakkakkaam.
formula _ 9
ivide soothravaakyam _ 10 ennathu thadassamillaatha taranga pravarthanamaanu. aswasthathayillaatha hamiltonian oormmikkumbol, nammal kaanunnu
soothravaakyam _ 11
aapekshika thiruthal kooduthal kanakkakkaan namukk eee phalam upayogikkaam
soothravaakyam _ 12
hydrajan aattathin,
formula _ 13 formula _ 14 umm formula _ 15 umm
soothravaakyam 16 praadhamika charge soothravaakyam 17 vaakvam permittivityum soothravaakyam 18 booar radiusumaanu, soothravaakyam 19 pradhana kwaandam number soothravaakyam 20 asimuthal kwaandam number soothravaakyam 21 nucleusil ninnulla electroninte dooravumaanu. athinaal, hydrajan aattathinte aadya oordar aapekshika thiruthal ithaanu
soothravaakyam _ 22
njangal evideyaanu upayogichathu
soothravaakyam _ 23
anthima kanakkukoottalil, graundu stettilekkulla aapekshika thiruthalinulla vyaapthiyude kramam formula _ 24 aanu.
spin-oorbitt coupling.
25 protonukalude (hydrajante soothravaakyam 26) soothravaakyam, bhramana koona chalana soothravaakyam 27, electron spin soothravaakyam 28 ennivayulla hydrajan polulla aattathin, spin-oorbitt padam nalkunnathu
soothravaakyam _ 29
ivide formula _ 30 ennathu spin jii-faaktaraanu.
staanderd frame oof referencil ninnu (electron nucleusine parikramanam cheiyunna) electron nischalamaaya sthalathekku maarunnathiloodeyum pakaram nucleus athine parikramanam cheiyunna sthalathekku maarunnathiloodeyum spin-oorbitt thiruthal manassilakkaan kazhiyum. eee saahacharyathil parikramanam cheiyunna nucleus oru phalapradamaaya karant looppayi pravartthikkunnu, athu oru kaanthikakshethram srishtikkum. ennirunnaalum, electroninu thanne athinte aantharika koneeya aavegam kaaranam oru kanthika moment undu. formula _ 31, formula _ 32 ennee rund kanthika vaahakangalum orumichu chernnaal avayude aapekshika aabhimukhyam anusarichu oru nischitha oorjja chelavu undaakum. ithu roopathinte oorjja thiruthalinu kaaranamaakunnu.
soothravaakyam _ 33
nucleus framil ninnu electroninte framilake maarunna aapekshika kanakkukoottalil ninnu varunna thomas presession ennu vilikkunna 2 nte oru pradhana ghadakam kanakkukoottalil cherkkendathundennu shradhikkuka.
annumuthal
soothravaakyam _ 34
kraamezhs-pasternack bandhangalum
soothravaakyam _ 35
hamiltoniante prathekshikkunna moolyam ithaanu
soothravaakyam _ 36
athinaal spin-oorbittal kaplinginte maagnittyoodinte kramam formula _ 37 aanu.
durbalamaaya baahya kaanthikakshethrangal prayogikkumbol, spin-oorbitt coupling seeman efakttinu kaaranamaakunnu.
darvin padam.
diarac samavaakyathinte aapekshikamallaatha vipuleekaranathil avasaanathe oru padamundu. chaals galton darvin aadyamaayi uruthirinjathinaal ithine darvin padam ennu vilikkunnu, ithu nalkiyirikkunnath
soothravaakyam _ 38
darvin padam ezz oorbittalukale maathrame baadhikkukayulloo. 39 enna soothravaakyamulla oru electroninte tharamgapravartthanam uthbhavasthaanath aprathyakshamaakunnathinaal deltta pravarthanatthinu oru falavumilla. udaaharanathinu, ithu 2s oorbitalinu 2p oorbittalinte athe oorjjam nalkunnu, 2s avasthaye uyarthunnu.
darvin enna padam electroninte pottensial energy maattunnu. electroninte sitterbevegang allengil drutha kwaandam aandolanangal moolam electrone nucleus thammilulla electrostaattik prathipravartthanathil ninnulla oru smeering aayi ithine vyaakhyaanikkaam. oru hraswa kanakkukoottaliloode ithu theliyikkaan kazhiyum.
anishchithathva thathwa soothravaakyam _ 40 prakaram kanakkaakkappedunna jeevithakalam kondu vertual electron-poositroon jodikal srishtikkaan kwaandam ettakkurachilukal anuvadikkunnu. eee samayat kanangalkk neengaan kazhiyunna dooram formula _ 41 aanu, ithu compton tharamgadairkhyamaanu. aattathinte electronukal aaa jodikalumaayi samvadikkunnu. ithu oru ettakkurachilukalla electron position formula _ 42 nalkunnu. oru tailor vipuleekaranam upayogichu, pottensial formula _ 43-leeii prabhavam kanakkakkaam
formula _ 44
ettakkurachilukalkku mukalilulla sharashari formula _ 45
formula _ 46
sharashari saadhyatha nalkunnu
soothravaakyam _ 47
ekadesha soothravaakyam _ 48, ithu ettakkurachilukal kaaranam pottanshyalinte aswasthatha srishtikkunnu
formula _ 49
mukalilulla padaprayogavumaayi thaarathamyam cheiyunnathinu, coolomb pottensial plug inn cheyyuka
soothravaakyam _ 50
ithu alpam vyathyasthamaan.
ezz-stettine maathram badhikkunna mattoru samvidaanam lamb shifttaanu, ithu kwaandam electrodynamicsile darvin padavumaayi thettidharikkappedaathu oru cheria thiruthalaanu. darvin padam ezz-avasthaykkum pii-avasthaykkum ore oorjjam nalkunnu, ennaal lamb shift pii-avasthayekkaal oorjjathil ezz-avasthaye uyarthunnu.
motham prabhavam.
muzhuvan hamiltonian nalkunnu
soothravaakyam _ 51
ivide coolomb prathipravartthanathil ninnulla hamiltonian formula _ 52 aanu.
moonnu gadakangale samgrahichukondu labhikkuna motham prabhavam inipparayunna padaprayogam nalkunnu
soothravaakyam _ 53
ivide formula _ 54 motham angular momentam kwaandam nambaraanu (formula _ 56 aanenkil formula _ 55 umm formula _ 57 umm). pazhaya booar sidhaanthathe adisthaanamaakki somerfeldaanu eee padaprayogam aadyamaayi nediyathu ennathu sradheyamaanu; i.iii.aadhunika kwaandam mechanics roopappeduthunnathinu munbu.
krithyamaaya aapekshika oorjjam.
diarac samavaakyam upayogichum motham prabhavam nedaanaakum. eee saahacharyathil, electronine aapekshikamallathathaayi kanakkakkunnu. krithyamaaya oorjjam nalkunnathu
soothravaakyam _ 58
mattu kanakkukoottalukalil ozhivakkiya ellah uyarnna krama padangalum ulkkollunna eee padaprayogam, perterbation sidhaanthathil ninnu uruthirinja oorjja thiruthalukal nalkunnathinu aadya kramatthilekku vikasikkunnu. ennirunnaalum, eee samavaakyathil nuclear spinumayulla edapedalukal moolamulla hyperfine ghadana thiruthalukal adangiyittilla. kwaandam feeld sidhaanthathil ninnulla mattu thiruthalukalaaya lamb shift, electroninte anomalus magnetic diapole moment enniva ulppeduthiyitla.

