
spin (bhouthika shaastram)

spin anedi praathamika kanaala dwara teesukuvellabade koneeya vegam yokka antargata roopam, tadwara hadronlu, anhu kendrakaalu mariyu anuvulu vanti mishrama kanaala dwara. spin nuu "tirige antargata dravyarashi" ardhamlo ardham chesukokudadu spin anedi parimaanaatmaka taranga lakshanam.
electron spin koneeya momentum unikini sturn-gerlach prayogam vanti prayogaala nundi oohinchabadindi, indulo vendi anuvulu kakshya koneeya momentum laenappatikee rendu saadhyamayye vivikta koneeya momentanu kaligi unnatlu gamaninchabaddaayi. electron spin unikini siddhaantaparamgaa spin-statistics siddhaantam nundi mariyu pauli minahaayimpu suutram nundi kooda oohinchavachhu-mariyu dheeniki viruddhamgaa, electron yokka nirdishta spin ichinatlayithe, pauli minahaayimpu suutraanni pondavacchu.
spin anedi ganitasaastraparamgaa photanla vanti konni kanaalaku vectorga mariyu electronla vanti itara kanaalaku spinnerlu mariyu bispinerlugaa varninchabadindi. spinnerlu mariyu bispinerlu vahakalu maadirigaane pravartistaayih avi khachitamaina parimaanaalanu kaligi untaayi mariyu bhramanaala krinda marutayi; ayithe, avi asaadhaaranamaina "disanu" upayogistaayi. icchina rakaniki chendina anni praathamika kanaalu oke parimaanamlo tirige koneeya vegaanni kaligi untaayi, ayithe daani dhisha maaravacchu. kanaaniki oka spin quantum sankhyanu ketayinchadam dwara ivi suuchimchabadataayi.
spin yokka sii unit shaastreeya koneeya momentum (i.ii., n·m·s, j·s, ledhaa kilolu·m2·s−1). aacharanalo, spin saadhaaranamgaa konarahita spin quantum sankhyagaa ivvabadutundi, idhi spin koneeya vegaanni taggina plank sthiraamkamtho vibhajinchadam dwara ivvabadutundi, idhi koneeya vegamtho samaanamaina kolatalanu kaligi untundi. tarachugaa, "spin quantum number" nuu kevalam "spin" anie pilustaaru.
shaastreeya bhramanaaniki sambandham.
electron spin kosam chaalaa prarambha namuunaalu tirige charge cheyabadina dravyaraasini oohinchaayi, conny vivaramgaa pariseelinchinappudu eee namuunaa viphalamavutundihi avasaramaina sthalam pampinhee electron vyaasaarthampai parimitulatoe saripoladu avasaramaina bhramana vegam kaanti vegaanni minchipotundi. praamaanika namoonaalo, praathamika kanaalannii "binduvu lantivi" gaa pariganinchabadataayih avi vaati chuttoo unna kshetram dwara vaati prabhavalanu kaligi untaayi. maas rotation aadhaaramgaa spin kosam edainaa modal aaa modaltho sthiramgaa undaali.
quantum spin kosam shaastreeya analog anedi kana taranga kshetramlo shakti ledhaa momentum-saandrata yokka prasaranah "spin anedi tappanisarigaa oka taranga aasti". spin yokka idhe bhavananu neetilo gurutvakarshana taramgaalaku vartimpajeyavachuhu "spin anedi neeti kanaala upa tarangadairghyam vruttaakaara kadalika dwara utpatti avutundi".
photan spin anedi kaanti dhruveekarana yokka quantum-yaantrika vivarana, ikkada spin + 1 mariyu spin-1 vruttaakaara dhruveekarana yokka rendu vyatiraeka disalanu suuchistaayi. anduvalla, nirvachinchabadina vruttaakaara dhruveekarana yokka kaanti oke spin thoo photaanlanu kaligi untundi, annee + 1 ledhaa annee-1. spin itara vector bosanlaku kooda dhruveekarananu suuchistumdi.
kakshya koneeya vaegaaniki sambandham.
paeru suuchimchinatlugaa, spin anedi modata oka aksham chuttoo oka kanamu yokka bhramanamgaa bhaavinchabadindi. chaaritraatmakamgaa kakshya koneeya vegam kana kakshyalaku sambandhinchinadi. yaantrika namuunaala aadhaaramgaa paerlu manugada saaginchinappatikii, bhouthika vivarana ledhu. parimaanaatmakata anedi praathamikamgaa spin mariyu arbital koneeya momentum rendinti yokka swabhaavaanni maarustundi. 
praathamika kanaalu binduvu lantivi kabatti, sweeya-bhramana anedi vatiki baga nirvachinchabadaledu. ayithe, spin anedi kanam yokka dasha suutram _ 1 gaa konampai aadharapadi untundani suuchistumdi, spin "s" kuu samaantaramgaa aksham chuttoo konam "θ" yokka bhramanam kosam. idhi sthithilo dasha aadharapadatam vanti momentum yokka quantum-yaantrika vivaranaku, mariyu koneeya sthithilo dasha aadharapadatam vanti kakshya koneeya momentum yokka vivaranaku samanam.
fermians kosam, chitram takkuva spashtamgaa untundi. koneeya vegam anedi hamiltonian yokka utpannam daani samyoga vaegaaniki ehrenfest siddhaantam dwara samanam, idhi mottam koneeya vaega operator. anduvalla, hamiltonian "h" spin "s" paie aadharapadi unte, "dh"/"ds" sunna kaanidi, mariyu spin koneeya vegaanni kaligistundi, anduvalla vaastava bhramanam, i.ii. kalakramena dasha-koona sambandhamlo maarpu. ayithe, idhi uchita electron kosam undaa anedi aspashtamgaa undhi, endukante oka electron kosam, "s" 2 sthiramgaa untundi, anduvalla hamiltonian atuvanti padaanni kaligi undaa anedi vivaranaku sambandhinchina vishayam. ayinappatikee, dirac sameekaranamlo spin kanipistundi, anduvalla electron yokka saapeksha hamiltonian, dirac feeldga pariganinchabadutundi, spin "la" loe aadharapadataanni kaluputuu ardham chesukovacchu. eee vivarana kinda, swechhaa electronlu kooda sweeya-bhramanaaniki lonavutaayi, eee bhramanamgaa jitterbegang prabhavanni ardham chesukuntaru.
quantum sankhya.
spin koneeya momentum quantisation yokka ganita niyamaalaku kattubadi untundi. spin angular momentum yokka nirdishta lakshanaalu
spin quantum sankhya yokka sampradaaya nirvachanam emitante, ikkada edainaa pratikuulam kaani puurnaamkam undavacchu. anduvalla anumatinchabadina viluvalu 0,1,2 modalainavi. praathamika kanaaniki viluva kanaala rakampai matrame aadharapadi untundi mariyu telisina vidhamgaa marchalemu (krinda vivarinchina "spin dhisha" kii viruddhamgaa). edainaa bhouthika vyavastha yokka spin koneeya vegam parimanatmakamga untundi. anumatinchabadina viluvalu
suutram _ 2
ekkada plank sthiraamkam, mariyu suutram _ 3 anedi taggina plank sthiraamkam. dheeniki viruddhamgaa, kakshya koneeya vegam anedi i yokka puurnaanka viluvalanu matrame teesukogaladu.ii., yokka sarri-sankhya viluvalu.
fermians mariyu bosans.
sagam-puurnaanka spinlu unna kanaalanu, udaaharanaku, fermians anie pilustaaru, ayithe 0,1,2 vanti puurnaanka spinlu unna kanaalanu bosans anie pilustaaru. kanaala yokka rendu kutumbaalu ververu niyamaalaku kattubadi untaayi mariyu mana chuttoo unna prapanchamlo "vistrutamgaa" ververu paatralanu kaligi untaayi. rendu kutumbaala madhya oka mukhya vyatyaasam emitante, fermians pauli minahaayimpu suutraaniki kattubadi untayih antey, oke quantum sankhyalanu ekakaalamlo kaligi unna rendu saaruupya fermians undakudadu (antey, sumaruga, oke sthaanam, vegam mariyu spin disanu kaligi undatam). fermians fermi-dirac ganaamkaala niyamaalanu paatistaayi. dheeniki viruddhamgaa, bosanlu boses-inestein ganaamkaala niyamaalaku kattubadi untaaru mariyu alanti parimiti ledhu, kabatti avi oke sthithilo "kalisi" undavacchu. alaage, mishrama kanaalu vaati bhaaga kanaala nundi bhinnamgaa tirugutaayi. udaaharanaku, naela sthithilo unna healium-4 anuvu spin 0 kaligi untundi mariyu daanini tayaaru chese kwarklu mariyu electronlu annee fermianlu ayinappatikee, bosan laaga pravartistundi.
idhi konni teevramaina parinaamaalanu kaligi untundih
spin-statistics siddhaantam.
spin-statistics siddhaantam kanaalanu rendu samuhaluga vibhajistundihi bosanlu mariyu fermians, ikkada bosanlu boses-inestein ganaamkaalanu paatistaayi, mariyu fermians fermi-dirac ganaamkaalanu (anduvalla pauli minahaayimpu suutram) paatistaayi. pratyekinchi, eee siddhaantam oka puurnaamkam tirige kanaalu bosanlu anie, ayithe anni itara kanaalu sagam-puurnaamkam tirigevi mariyu fermianlu anie chebutundi. udaaharanaku, electronlu sagam-puurnaanka spin kaligi untaayi mariyu avi pauli minahaayimpu suutraaniki kattubadi unde fermians, ayithe phootaanlu puurnaanka spin kaligi untaayi mariyu kaligi undavu. eee siddhaantam quantum mechanics mariyu pratyeka saapekshata siddhaantam rendintipai aadhaarapadutundi, mariyu spin mariyu ganaamkaala madhya eee sambandhaanni "pratyeka saapekshata siddhaantam yokka atyanta mukhyamaina anuvartanaallo okati" anie pilustaaru.
ayaskanta kshanaalu.
saampradaaya electrodynamicslo tirige vidyut aavesam kaligina sareeram vale, spin unna kanaalu ayaskanta dvidhruva kshanaanni kaligi untaayi. eee ayaskanta kshanaalanu aneka vidhaluga prayogaatmakamgaa gamaninchavacchu, udhaa.zii. sturn-gerlach prayogamlo asamaana ayaskanta kshetraala dwara kanaala vikshepam dwara ledhaa kanaala dwara utpatti cheyabadina ayaskanta kshetraalanu kolavadam dwara.
chaarj, maas mariyu spin koneeya momentamtho kuudina spin-partical yokka antargata ayaskanta kshanam,
ikkada parimaanam laeni parimaanaanni spin-phyaaktar antaaru. pratyaekamgaa kakshya bhramanaala kosam idhi 1 avutundi (dravyarashi mariyu charge samaana vyaasaartham gala golaalanu aakramistaayani bhaavinchi).
electron, charge cheyabadina praathamika kanam kaavadamtho, sunna kaani ayaskanta kshanaanni kaligi untundi. quantum electrodynamics siddhaantam yokka vijayalalo okati electron-karakam yokka khachitamaina anchanaa, idhi oka praamaanika vichalanam vadda chivari rendu ankelalo kolata anischitini soochinche kundaleekaranaalalo ankelatho, viluvanu kaligi undataaniki prayogaatmakamgaa nirnayinchabadindi. 2 yokka viluva diarock sameekaranam nundi utpannamavutundi, idhi electron yokka spin nuu daani vidyudayaskaanta lakshanaalatoo anusandhaaninche praathamika sameekaranam, mariyu daani swantha kshethramtho sahaa chuttupakkala vidyudayaskaanta kshethramtho electron yokka paraspara charya nundi vichalanam utpannamavutundi.
mishrama kanaalu vaati bhramanamtho anubandhinchabadina ayaskanta kshanaalanu kooda kaligi untaayi. mukhyamgaa, neutron vidyut tatasthamgaa unnappatikee sunna kaani ayaskanta kshanaanni kaligi untundi. neutron praathamika kanam kaadani eee vaastavam prarambha suuchana. vaastavaaniki, idhi vidyut chaarj kanaalu ayina kwarklatho tayaaravutundi. neutron yokka ayaskanta kshanam vyaktigata kwarkla spinla nundi mariyu vaati kakshya kadalikala nundi vastundi.
neutrinolu praathamika mariyu vidyut tatastha rendoo. sunna kaani neutrino dravyaraasini parigananaloki teesukune kaneesa podiginchina praamaanika namuunaa neutrino ayaskanta kshanaalanu anchanaa vestundihi
neutrino ayaskanta kshanaalu, neutrino dravyarashi, mariyu bohr magneton ekkada untaayi. ayithe, vidyudayaskaanta sthaayi kante kotta bhouthika shaastram gananeeyamgaa ekkuva neutrino ayaskanta kshanaalaku daariteestundi. sumaru 10−14 kante pedda neutrino ayaskanta kshanaalu "asahajamainavi" anie oka namuunaa-swatantra maargamlo chuupavachchu, endukante avi neutrino dravyaraasiki pedda vikirana sahakaaraaniki kooda daariteestaayi. neutrino dravyarashi dadapuga unnatlu telisinanduna, vikirana diddubatla dwara neutrino dravyaraasiki pedda mottamlo dohadapadataanni nivaarinchadaaniki chakkati-tuning avasaram. neutrino ayaskanta kshanaala kolata anedi parisoedhana yokka kriyaaseela praantam. prayogaatmaka phalitaalu neutrino ayaskanta kshanaanni electron ayaskanta kshanam kante takkuva saarlu unchaayi.
marovaipu, vidyutcharj laeni, conny spin thoo unna praathamika kanaalu, photan ledhaa z bosan vanti vatiki ayaskanta kshanam undadu.
curie ushnograta mariyu amarika nashtam.
saadhaarana padaarthaalalo, vyaktigata anuvula ayaskanta dvidhruva kshanaalu okadaanikokati raddu chese ayaskanta kshetraalanu utpatti chestaayi, endukante prati dvidhruva binduvu yaadruchchika disalo untundi, mottam sagatu sunnaki chaalaa daggaragaa untundi. ayithe, vaati curie ushnograta kante takkuva unna pheromagnetic padaarthaalu ayaskanta domainlanu pradarsistaayi, dheenilo anhu dvidhruva kshanaalu sthaanikamgaa yaadrucchikamgaa samalekhanam avtayi, domine nundi sthuula, sunna kaani ayaskanta kshetraanni utpatti chestaayi. ivi manandarikee telisina saadhaarana "ayaskaantaalu".
paramagnetic padaarthaalalo, vyaktigata anuvula ayaskanta dvidhruva kshanaalu baahyamgaa vartinche ayaskanta kshethramtho paakshikamgaa samalekhanam avtayi. ayaskanta padaarthaalalo, marovaipu, vyaktigata anuvula ayaskanta dvidhruva kshanaalu, shakti avasaramaite kooda, edainaa baahyamgaa vartinche ayaskanta kshetraaniki viruddhamgaa samalekhanam avtayi.
atuvanti "spin namuunaala" pravartana yokka adhyayanam ghaneebhavinchina padaartha bhouthika saastramlo parisoedhana yokka abhivruddhi chendutunna praantam. udaaharanaku, icing modal rendu saadhyamaina sthithulanu matrame kaligi unna spinlanu (diapols) vivaristundi, paiki krindiki, ayithe heisenberg namoonaalo spin vector yea disalo ayina choopinchadaaniki anumatinchabadutundi. eee namuunaalu aneka aasaktikaramaina lakshanaalanu kaligi unnaayi, ivi dasha parivartana siddhaantamlo aasaktikaramaina phalitaalaku daariteesaayi.
dhisha.
spin projection quantum sankhya mariyu gunakaaram.
shaastreeya yantrasaastramlo, oka kanapu koneeya vegam parimaanaanni (sareeram entha vaegamgaa tirugutundo) matrame kakunda, oka disanu (kana bhramana aksham meeda paiki ledhaa krindiki) kooda kaligi untundi. quantum-mechanical spin kooda dhisha gurinchi samacharanni kaligi untundi, conny marinta suukshmamaina roopamlo untundi. quantum mechanics prakaram, yea disalo kolichina spin-"s" kanaaniki koneeya momentum yokka bhaagam viluvalanu matrame teesukogaladu
ikkada-th aksham venta spin bhaagam (ledhaa, ledhaa),-th aksham venta spin projection quantum sankhya, mariyu pradhana spin quantum sankhya (munupati vibhaagamlo charchinchabadindi). saampradayakamgaa enchukunna dhisha aksham.
aksham venta spin bhaagam ekkada undhi, aksham venta spin projection quantum sankhya.
saadhyamayye viluvalu unnayani chudavachu. sankhya" anedi spin vyavastha yokka gunakaaram. udaaharanaku, oka spin-partical kosam rendu saadhyamaina viluvalu matrame unnaih mariyu. ivi quantum sthithulaku anugunamgaa untaayi, dheenilo spin bhaagam varusaga + "z" ledhaa − "z" disalalo chooputundi, mariyu tarachugaa "spin up" mariyu "spin down" gaa suuchistaaru. delta baryon vanti spin-partical kosam, saadhyamayye viluvalu +, +, −, −.
vector.
icchina quantum sthithiki, oka spin vector formula _ 8 gurinchi aalochinchavachhu, dheeni bhagalu prati aksham venta spin bhagala yokka anchanaa viluvalu, i.ii.suutram _ 9. eee vector appudu bhramanam yokka aksham yokka shaastreeya bhavanaku anugunamgaa, spin chuuputunna "dhisha" nuu vivaristundi. vaastava quantum-yaantrika gananalalo spin vector chaalaa upayogakaramgaa ledani, endukante dheenini neerugaa kolavalemu, mariyu vaati madhya quantum anischiti sambandham kaaranamgaa ekakaalamlo khachitamaina viluvalanu kaligi undalemu. ayithe, sturn-gerlach upakaranam vadakam dwara adhe swachchamaina quantum sthithilo unchabadina kanaala ganankaparamga pedda sekaranalaku, spin vector baga nirvachinchabadina prayogaatmaka ardhaanni kaligi untundih idhi saadhaarana pradaesamloe disanu nirdesistundi, dheenilo sekaranaloni prati kanaanni gurtinche garishta sambhaavyata (100%) saadhinchadaaniki tadupari detector tappanisarigaa oriented ayi undaali. spin-kanaala kosam, spin vector mariyu detector madhya konam perige koddi eee sambhaavyata sajavuga taggutundi, 180° konam varaku-antey, spin vektarku vyatiraeka disalo unna detectorla kosam-sekarana nundi kanaalanu gurtinche nireekshana kaneesam 0 saataaniki cherukuntundi.
gunaatmaka bhavanaga, spin vector tarachugaa upayogakaramgaa untundi endukante idhi saastriiyamgaa chithreekarinchadam sulabham. udaaharanaku, quantum-mechanical spin shaastreeya gyroscopic prabhaavaalaku saaruupyamaina drugvishayaanni pradarsinchagaladu. udaaharanaku, oka electronnu ayaskanta kshetramlo unchadam dwara oka rakamaina "tark" nuu upayoginchavacchu (eee kshetram electron yokka antargata ayaskanta dvidhruva kshanam meeda panichestundi-eee krindi vibhaganni chudandi). phalitamgaa, spin vector oka shaastreeya gyroscope maadirigaane mundugaane jarugutundi. eee drugvishayaanni electron spin resonance (esr) anie pilustaaru. anhu kendrakaalalo protanla samaanamaina pravartananu nuclear magnetic resonance (nmr) spectroscopy mariyu imaginglo upayogistaaru.
ganitasaastraparamgaa, quantum-yaantrika spin sthithulanu spinnerlu anie piluvabade vector lanty vastuvula dwara vivaristaaru. samanvaya bhramanaala krinda spinnerlu mariyu vahakalu yokka pravartana madhya suukshmamaina thedaalu unnaayi. udaaharanaku, oka spin-kanaanni 360° dwara tippadam anedi adhe quantum sthithiki tirigi teesukuraadu, conny vyatiraeka quantum dasato sthithiki teesukuvastundi; idhi suutrapraayamgaa, jokyam prayogaalato gurtinchadaginadi. kanaanni daani khachitamaina asalu sthithiki tirigi teesukuraavadaaniki, 720° bhramanam avasaram. (plate trick mariyu mobius strip naan-quantum saaruupyatalanu istayi.) oka spin-jeero kanaaniki tark vartimpajesina tarvaata kooda oke quantum sthithi untundi. oka spin-2 kanaanni 180° tippadam valla adhi tirigi adhe quantum sthithiki teesukuraagaladu, mariyu oka spin-4 kanaanni adhe quantum sthithiki tirigi teesukuraavadaaniki 90° tippali. spin-2 kanaanni 180° tippina tarvaata kooda oke vidhamgaa kanipinche oka strait sticku saaruupyata kaligi undavacchu, mariyu spin-0 kanaanni golamgaa oohinchavachhu, idhi yea konam gundaa tirigina tarvaata adhe vidhamgaa kanipistundi.
ganita suutram.
operator.
kakshya koneeya vaegaaniki saaruupyamaina parivartana sambandhaalanu spin paatistundih
levi-poura chihnam ekkada undhi? idhi suutram _ 11 mariyu suutram _ 12 (mottam praatipadikana ketlugaa vyakteekarinchabadindi) yokka aigen vectors (koneeya momentum maadirigaa) nuu anusaristundi.
eee aigen vektarlapai panichese spin rising mariyu loying operatorlu istaaru
suutram _ 15 ekkada undhi.
conny kakshya koneeya vegavantam vale kakunda, igenvectorlu golaakaara samarasyam kaadu. avi mariyu yokka vidhulu kaavu. mariyu yokka sagam-puurnaanka viluvalanu minahaayinchadaaniki kooda etuvanti kaaranam ledhu.
anni quantum-yaantrika kanaalu antargata spin suutram _ 16 nuu kaligi untaayi (ayithe eee viluva sunnaki samanamga undavacchu). edainaa aksham meeda spin formula _ 16 yokka projection taggina plank sthiraamkam yokka unitlalo parimaanam cheyabadutundi, antey kanaala yokka sthithi function, suutram _ 18 kaadu, conny suutram _ 19, ikkada suutram _ 20 krindi vivikta samiti yokka viluvalanu matrame teesukogaladuh
okati bosanlu (puurnaamkam spin) mariyu fermians (sagam-puurnaamkam spin) lanu vaeru chestundi. paraspara charya prakriyalalo samrakshinchabadina mottam koneeya vegam appudu kakshya koneeya vegam mariyu spin yokka mottam.
pauli metricals.
spin-observables thoo anubandhinchabadina quantum-mechanical operatorlu
cartician bhagalalo ekkada
spin-kanaala pratyeka sandarbham kosam, mariyu moodu pauli maatrikaluh
pauli minahaayimpu suutram.
okela unde kanaala vyavasthalaku idhi pauli minahaayimpu suutraaniki sambandhinchinadi, idhi daani taranga kriya suutram _ 25 anedi edainaa rendu kanaala paraspara maarpula meeda maaraali anie perkondi.
anduvalla, bosanlaku prefactor + 1kii taggutundi, fermiansku −1kii taggutundi. quantum mechanicslo anni kanaalu bosanlu ledhaa fermians avtayi. konni oohaatmaka saapeksha quantum kshetra siddhaantaalalo "supersimetric" kanaalu kooda unnaayi, ikkada bosonic mariyu fermionic bhagala sarala kalayikalu kanipistaayi. rendu kolatalalo, prefactornu yea ayanlonaina parimaanam 1 yokka sanklishta sankhyatho bharti cheyavachu.
paina perkonna kramaparivartana-kana sthithi vidhula kosam anubhavamu rojuvaaree jeevitamlo atyanta mukhyamaina parinaamaalanu kaligi untundi, udhaa.zii. rasayana muulakaala aavartana pattika.
bhramanaalu.
paina vivarinchinatlugaa, quantum mechanics prakaram, yea disalo kolichina koneeya momentum yokka bhagalu aneka vivikta viluvalanu matrame teesukogalavu. anduvalla, kanaala spin yokka atyanta anukuulamaina quantum-yaantrika vivarana anedi icchina akshampai daani antargata koneeya momentum yokka projection yokka icchina viluvanu kanugone amplitudelaku anugunamgaa sanklishta sankhyala samititoe untundi. udaaharanaku, oka spin-partical kosam, manaku rendu sankhyalu avasaram, idhi koneeya momentum yokka projection thoo daanini kanugone amplitudelanu istundi, idhi avasaranni santruptiparustundi.
spin thoo kuudina saadhaarana kanaaniki, manaku atuvanti paaraamitulu avasaram. eee sankhyalu aksham yokka empikapai aadharapadi untaayi kabatti, eee aksham tiriginappudu avi okadaanikokati chinnaviga marutayi. parivartana chattam saralamgaa undaali anedi spashtamgaa undhi, kabatti prati bhramanamtho oka maatrikanu anubandhinchadam dwara manam daanini suuchimchavachchu, mariyu bhramanaalaku sambandhinchina rendu parivartana maatrikala utpatti a mariyu b anedi bhramanam ab nii soochinche maatrikaku samanamga (dasha varaku) undaali. inca, bhramanaalu quantum-yaantrika antargata utpattini samrakshistaayi, alaage mana parivartana maatrikalu kooda undali
ganitasaastraparamgaa cheppalante, eee maatrikalu bhramana samuuham yokka ekaatmaka prakshepaka praatinidhyaanni andistaayi kabatti (3). atuvanti prati praatinidhyam suu (2) anae cover group yokka praatinidhyaaniki anugunamgaa untundi. prati dimensionku suu (2) yokka oka dimension irreducible representation undhi, ayithe eee representation anedi besi kosam-dimension real mariyu eeven kosam-dimension complexes (anduvalla real dimension). saadhaarana vector suutram _ 30 thoo samatalamlo konam dwara bhramanam kosam,
ikkada suutram _ 32, mariyu idhi spin operatorla vector.
euler koonaalanu upayoginchi eee rakamaina sammelanam operatorla dwara trimiteeya sthalamlo saadhaarana bhramanaanni nirminchavachuhu
eee operatorla samuuham yokka irreducible praatinidhyam wigner dii-matricks dwara andinchabadutundih
ekkada
idhi wigner yokka chinna dii-matricks. mariyu kosam gamaninchandi; i.ii., aksham chuttoo puurti bhramanam, wigner dii-matricks muulakaalu avtayi
oka saadhaarana spin sthithini khachitamaina sthithula superpositionga vraayavacchani gurthuchesukunte, oka puurnaamkam ayithe, anni viluvalu puurnaamkaalu anie mariyu eee maatruka gurtimpu operatorku anugunamgaa untundani manam chustamu. ayithe, sagam-puurnaamkam ayithe, viluvalu kooda sagam-puurnaamkaalu, andarikee istayi, anduvalla 2 dwara tirigina taruvaata rashtram mainus gurtunu enchukuntundi. eee vaastavam spin-statistics siddhaantam yokka rujuvulo keelakamaina amsam.
lorentz parivartanalu.
saadhaarana lorentz parivartanala krinda spin yokka pravartananu nirnayinchadaaniki manam adhe vidhananni prayatninchavacchu, conny manam ventane oka pedda addankini kanugontamu. kabatti (3) kakunda, lorentz parivartanala samuuham kabatti (3,1) compact kaanidi mariyu anduvalla etuvanti nammakamaina, ekaatmaka, parimita-dimensional praatinidhyaalu laevu.
spin-kanaala vishayamlo, parimita-dimensional praatinidhyam mariyu eee praatinidhyam dwara samrakshinchabadina scalar utpatti rendintinee kaligi unna nirmaanaanni kanugonadam saadhyamavutundi. prati kanamtho 4-bhagala diarock spinarnu anubandhistaamu. eee spinnerlu chattam prakaram lorentz parivartanala krinda marutayi
ikkada gaama maatrikalu unnaayi, mariyu idhi parivartananu niyantrinche antisemetric 4 × 4 maatrika. scalar utpatti anie chuupavachchu
samrakshinchabadindi. ayithe, idhi saanukuula-khachitamainadi kaadu, kabatti praatinidhyam ekaatmakamainadi kaadu.
, ledhaa akshaala venta tirige kolata.
spin-kanaala (hermician) pauli maatrikalalo pratidaaniki + 1 mariyu −1 anae rendu aigen viluvalu untaayi. sambandhita normalised igenvectorlu
quantum mechanics yokka postulates dwara, electron spin nuu kolavadaniki roopondinchina oka prayogam, ledhaa aksham, aaa aksham meeda sambandhita spin operator (, ledhaa) yokka aigen viluvanu matrame istundi, i.ii. ledhaa. oka kanamu yokka quantum sthithini (spinku sambandhinchi), rendu-bhagala spinner dwara suuchimchavachchuh
eee kanapu spin icchina akshaniki sambandhinchi kolichinappudu (eee udaaharanalo, aksham), daani spin kevalam suutram _ 41 gaa koliche sambhaavyata. tadanugunamgaa, daani spin kevalam suutram _ 42 gaa koliche sambhaavyata. kolata taruvaata, kana yokka spin sthithi sambandhita aigen stateloki koolipotundi. phalitamgaa, icchina aksham venta kanaala spin icchina aigen viluvanu kaligi undela kolichinatlayithe, anni kolatalu oke aigen viluvanu istayi (suutram _ 43, modalainavi nundi.), itara akshaala venta spin yokka kolatalu cheyabadavu.
ekapaksha aksham venta tirige kolata.
ekapaksha aksham disalo spin koliche operator pauli spin maatrikala nundi sulabhamgaa pondavacchu. ekapaksha unit vectorga undanivvandi. appudu eee disalo spin kosam operator kevalam
operator saadhaarana spin maatrikala maadirigaane aigen viluvalanu kaligi untundi. ekapaksha disalo spin kosam operatornu kanugone eee paddhati adhika spin statesku saadhaaraneekaristundi, mugguru operatorla vector thoo dhisha yokka dott productnu moodu-,-,-axis disalaku teesukuntundi.
disalo spin kosam oka saadhaarana spinner (idhi spin down tappa anni spin statesku panichestundi, idhi ekkada istundi)
matricksnu vikarnam cheyadam dwara mariyu aigen viluvalaku anugunamgaa igenstatelanu kanugonadam dwara paina perkonna spinar saadhaarana maargamlo pondabadutundi. quantum mechanicslo, vektarlanu normalising factortho guninchinappudu "normalised" anie pilustaaru, dheeni phalitamgaa vector aikyata yokka podavunu kaligi untundi.
spin kolatala anukuulata.
pauli maatrikalu prayaaninchavu kabatti, vividha akshaala venta tirige kolatalu ananukuulamgaa untaayi. dheeni ardham, udaaharanaku, aksham venta tirigedi manaku teliste, aapai aksham venta tirigedi kolichinatlayithe, aksham chuttoo tirige mana munupati gnaanaanni chellanidigaa chesaamu. dheenini aigen vectors yokka aasti nundi chudavachu (i.ii. pauli maatrikala yokka igenstatelu)
kabatti bhouthika saastravettalu aksham venta oka kanapu spin nuu kolichinappudu, udaaharanaku, kanapu spin state igenstate formula _ 47 loki koolipotundi. taruvaata manam aksham venta kanaala spin nuu kolichinappudu, spin state ippudu formula _ 48 ledhaa formula _ 49 gaa koolipotundi, prati okkati sambhaavyatatoo untundi. mana udaaharanalo, manam kolustaamu anie cheppandi. ippudu manam aksham venta kanaala spin nii mallii kolavadaniki tirigi vachinappudu, manam koliche ledhaa prati okkati unde sambhaavyatalu (i.ii. avi varusaga suutram _ 50 mariyu suutram _ 51). idhi aksham venta tirige asalu kolata ikapai chellubaatu kaadani suuchistumdi, endukante aksham venta tirige kolata ippudu samaana sambhaavyatatoo aigen viluvanu kaligi undataaniki kolustaaru.
adhika spinlu.
spin-operator anedi suu (2) yokka praathamika praatinidhyaanni yerparustundi. eee praatinidhyam yokka kronekar utpattulanu padepade teesukovadam dwara, evarainaa anni adhika irreducible praatinidhyaalanu nirminchavacchu. antey, moodu praadaesika kolatalalo adhika-spin vyavasthala kosam phalitamgaa vachhe spin operatorlanu eee spin operator mariyu nicchena operatorlanu upayoginchi ekapakshamgaa peddadigaa lekkinchavacchu. udaaharanaku, rendu spin-kronekar utpattini teesukunte naalugu dimensional praatinidhyaanni istundi, idhi trimiteeya spin-1 (triple states) mariyu 1 dimensional spin-0 praatinidhyamgaa (single state) vaeru cheyabadutundi.
phalitamgaa irreducible praatinidhyaalu z-basis loe krindi spin maatrikalu mariyu aigen viluvalanu istaih
 0 & 1 & 0 \\
 1 & 0 & 1 \\
 0 & 1 & 0
 \end {pmatrix}, &
 \edama|1, + 1 \Rect\Rangle _ x & = \frac {1} {2} \start {pmatrix} 1\\ {\sqrt {2}}\\ 1\end {pmatrix}, &
 \edama|1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x, x, x, x &
 \edama|1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-1, - \\
 0 &-i & 0 \\
 i & 0 &-i \\
 0 & i & 0
 \end {pmatrix}, &
 \edama|1, + 1, \Rect\Rangle _ y & = \frac {1} {2} \start {pmatrix}-1\- i\sqrt {2}\\1\end {pmatrix}, &
 \edama|1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 &
 \edama|1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-2,-1,-2,-1,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1, - \\
 s _ z & = \hbar
 1 & 0 & 0 \\
 0 & 0 & 0 \\
 0 & 0 &-1
 \end {pmatrix}, &
 \edama|1, + 1 \Reft\Rangle _ z & = \start {pmatrix} 1\\ 0\0 \end {pmatrix}, &
 \edama|1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 &
 \edama|1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1, - \\
\mugimpu {samalekhanam} </ganitam>
suutram _ 52
suutram _ 53
suutram _ 54
ikkada suuchikala suutram _ 55 anedi puurnaanka sankhyalu
suutram _ 56
bahula kana vyavasthala quantum mechanicslo kooda upayogakaramgaa, saadhaarana pauli samuuham pauli maatrikala yokka anni-retlu tensor utpattulanu kaligi undataaniki nirvachinchabadindi.
pauli maatrikala paramgaa euler suutram yokka analog suutram
adhika spinlaku tractable, conny takkuva sulabham.
samaanatvam.
kendrakaalu ledhaa kanaala kosam spin quantum sankhya yokka pattikalalo, spin tarachugaa "+" ledhaa "−" dwara anusarinchabadutundi. idhi sarri samaanatvam kosam "+" thoo samaanatvaanni suuchistumdi (praadaesika vilomam dwara maarani taranga function) mariyu besi samaanatvam kosam "−" (praadaesika vilomam dwara vyatirekinchabadina taranga function). udaaharanaku, bismat yokka isotopulanu chudandi, dheenilo isotopula jaabitaalo kaalam nuclear spin mariyu parity untaayi. dvi-209 kosam, ekkuva kaalam jeevinchina isotope, 9/2-pravesam antey anhu spin 9/2 mariyu samaanatvam besi anie ardham.
applications.
spin mukhyamaina saiddhaantika chikkulu mariyu aacharanaatmaka anuvartanaalanu kaligi undhi. spin yokka baga sthirapadina "pratyaksha" anuvartanaaluh
electron spin ayaskaantatvamloo mukhyamaina paatra poeshistumdi, udaaharanaku computer memarylalo anuvartanaalu. radeo-frequency taramgaala (nuclear magnetic resonance) dwara "nuclear spin" nuu taarumaaru cheyadam rasayana spectroscopy mariyu vaidya imaginglo mukhyamainadi.
spin-arbit coupling anhu varnapatam yokka chakkati nirmaanaaniki daariteestundi, idhi anhu gadiyaralalo mariyu rendava aadhunika nirvachanamlo upayoginchabadutundi. electron yokka-karakam yokka khachitamaina kolatalu quantum electrodynamics yokka abhivruddhi mariyu dhruvikaranalo mukhyamaina paatra poeshinchaayi. "photan spin" anedi kaanti dhruveekarana (photan dhruveekarana) thoo mudipadi untundi.
spin transisterlalo binary information carrierga spin yokka abhivruddhi chendutunna anuvartanam. 1990loe pratipaadinchabadina asalu bhavananu dattaa-daas spin transister anie pilustaaru. spin transisterla aadhaaramgaa electronicsnu spintronics anie pilustaaru. metal-doped john ledhaa teo2 vanti paluchana ayaskanta semiconductor padaarthaalalo spin yokka taarumaaru marinta swechhanu istundi mariyu marinta samarthavanthamaina electronics kalpananu sulabhataram chese saamarthyaanni kaligi untundi.
rasayana shaastram yokka aavartana pattikatho praarambhamayye aneka "paroksha" anuvartanaalu mariyu spin mariyu anubandha pauli minahaayimpu suutram yokka vyakteekaranalu unnaayi.
charitra.
kshaara lohala udgaara varnapatam sandarbhamlo spin modata kanugonabadindi. 1924loe, wolfgang pauli, atyanta bayati shell looni electrontho anubandhinchabadina "saastriiyamgaa varninchaleni rendu-viluvala" nii pravesapettaadu. idhi oke quantum vyavasthalo yea rendu electronlu oke quantum sthithini kaligi undavani paerkontuu pauli minahaayimpu suutraanni roopondinchadaaniki ataniki veelu kalpinchindi.
pauli yokka "degree off friedam" yokka bhouthika vivarana modatlo teliyadu. landey sahayakulalo okaraina ralf cronig, 1925 praarambhamlo electron yokka sweeya-bhramana dwara utpatti cheyabadindani suuchimchaadu. pauli eee aalochana gurinchi vinnapudu, daanini teevramgaa vimarsinchaadu, electron yokka oohaatmaka uparitalam kaanti vegam kante vaegamgaa kadulutuu undalsi untundani, adhi avasaramaina koneeya vegaanni utpatti cheyadaaniki taginanta vaegamgaa tirugutundani paerkonnaadu. idhi saapeksha siddhaantaanni ullanghistundi. ekkuvagaa pauli vimarsala kaaranamgaa, cronig thana aalochananu prachurinchakuudadani nirnayinchukunnadu.
1925 saradrutuvulo, dutch bhouthika saastravettalu georg uhlenbeck mariyu leiden vishwavidhyaalayamlo shamyul goudsmitlaku adhe aalochana vachindi. paal ehrenfest salaha meraku vaaru tama phalitaalanu prachurinchaaru. idhi anukuulamaina pratispandananu pondindi, mukhyamgaa levelin thamus prayogaatmaka phalitaalu mariyu uhlenbeck mariyu goudsmit gananala (mariyu cronig yokka prachurinchani phalitaalu) madhya rendu vyatyaasaala karakanni parishkarinchagaligina taruvaata. eee vyatyaasam electron yokka sparsaka chatram yokka dhorani kaaranamgaa, daani sthaanaaniki adanamgaa undhi.
ganitasaastraparamgaa cheppalante, fiber bundle vivarana avasaram. sparsaka bundle prabhavam sankalitam mariyu saapekshamainadi; antey, anantaniki velithe adhi adrusyamavutundi. idhi sparsha-antariksha dhoraniki sambandhinchi pondani viluvalo sagam, conny vyatiraeka gurtuto untundi. eee vidhamgaa mishrama prabhavam rendava karakam (thamus precession, 1914loe ludwick sylbersteinku telisinadi) dwara rendodaaniki bhinnamgaa untundi.
thana prarambha abhyantaraalu unnappatikee, 1927loe shroadinger mariyu heisenberg kanugonna quantum mechanics yokka aadhunika siddhaantaanni upayoginchi pauli spin siddhaantaanni lanchanaprayamga roopondinchaadu. athanu spin operatorla praatinidhyamgaa pauli maatrikalanu upayoginchadamlo maargadarsakatvam vahinchaadu mariyu rendu-bhagala spinner taranga-functionnu pravesapettaadu. uhlenbeck mariyu goudsmit sampradaaya bhramana nundi utpannamayye spin gaa pariganinchaaru, ayithe pauli spin anedi shaasthreeyam kaani mariyu antargata aasti anie nokki chepparu.
pauli yokka spin siddhaantam saapekshataavaadam laenidi. ayithe, 1928loe, paal dirac dirac sameekaranaanni prachurinchaadu, idhi saapeksha electronnu vivarinchindi. diarock sameekaranamlo, electron taranga-function kosam naalugu-bhagala spinner ("diarock spinner" anie pilustaaru) upayoginchabadindi. saapeksha spin gyromagnetic kramaraahityaanni vivarinchindi, dheenini (puurva veekshanhalo) 1914loe shamyul jackson barnet modatisaarigaa gamaninchaaru (inestein-dii haas prabhavam chudandi). 1940loe, pauli "spin-statistics siddhaantam" nuu niroopinchaadu, idhi fermiansku sagam-puurnaamkam spin mariyu bosanlaku puurnaamkam spin untundani perkondi.
venakki tirigi choosthe, electron spin yokka modati pratyaksha prayogaatmaka sakshyam 1922 naati sturn-gerlach prayogam. ayithe, eee prayogaaniki saraina vivarana 1927loe matrame ivvabadindi.

