3-jeey chinh

quantum yantrikimadhye, 3 "-jeey. emm." chinhe mhanoonahi olakhali jaanari wigner 3-jeey chinhe, koneey moment jodanyachya uddeshane clebsch-gorden gunankanna paryay aahet. donhi drushtikon agadi samaan bhautik samasyeche nirakaran karat asatana, 3-"jeey" chinhe adhik samamitiyapane karatat.
clebsh-gorden gunankanshi ganiteey sambandh.
3-'jeey' chinhe clebsh-gorden gunankanchya sandarbhat dilee jaatat
jeey" aanee "emm" ghatak heey koneey-gatiman quantum sankhya aahet, i.eae.pratyek (aanee pratyek sambandhit) ektar eka nakaratmak nasalela purnank kinwa ardh-visham-purnank asato. chinh ghatakacha ghatank nehmich eka purnank asato, mhanoon davikade sthanantar kelyavar too sarkhach rahato aanee paryay kelyavar ulat sambandh yetoh
clebsh-gorden gunankanshi paribhashit sambandh.
see. jee. gunank paribhashit kele jaatat jenekarun done koneey momentanchi berries berries drushtine vyakt hoilah
dusarikade, 3-'jeey' chinhe heey gunank aahet jyanchyabarobar teen koneey moment jodane aavashyak aahe jenekarun parinami shoonya hoilah
yethe sootra 5 hii shoonya-aayatakruti-gatee sthitee aahe (sootra 6). heey spasht aahe qee 3-'jeey' chinh jode samasyemadhye samavisht asalelya tinhi koneey kshananna samaan payarivar hatalate aanee mhanoon teey see. jee. gunankapeksha adhik samamiteey aahe.
sthitee sootra _ 5 heey paribhramanadvare badalat naslyamule, 3-'jeey' chinh asalelya teen paribhraman avasthanchya gunakaranche aakunchan paribhramanannusar aparivartaniy aahe asehi mhanatat.
nivadiche niyam.
yaa serve atty purn jhalyashivay wigner 3-"jeey" chinh shoonya aaheh
samamiti gunadharm.
3-'jeey' chinh tyachya stambhanchya summ kramparivartanakhali aparivartaniy aaheh
stambhanche visham kramparivartan eka tappa ghatak deteh
11 quantum sankhya () yaa sutrache chinh badalalyane dekhil eka tappa midatoh
3-'jeey' chinhanmadhye tathakathit rej samamiti dekhil asatat, jyaa kramparivartan kinwa vel ulatanyamule nasatat. yaa samamiti aaheth
rej samamitisah, 3-'jeey' chinhamadhye ekoon 72 samamiti aahet. heey rej chinhachya vyakhyedvare sarvottampane pradarshit kele jaatat, jeey tyachya aanee 3-'jeey' chinhachya darmyan eka-teey-eka sanvad aahe aanee ardh-jaduchya chaurasache gunadharm gruheet dharteh
jyadvare 72 samamiti aata 3 shhee sambandhit aahet! rang aanee 3! stambh paraspar vinimay aanee matrixche sthanantar. yaa tathyancha vapar prabhavi sathavan yojana tayar karnyasathi keela jaau shakato.
orthogonality sambandh.
pariman asaleli done koneey momentanchi pranali aanee ektar naan jodalya gelelya besis states (quantum numbers aanee label kelelya) kinwa coupled besis states (label kelelya aanee) chya drushtine varnan kele jaau shakate. 3-'jeey' chinhe yaa done payanmadhye ekatmak parivartan ghadavatat aanee hii ekatmata orthogonality sambandh soochit karate.
jevha trikoni tribhuj ("jeey" 1 "," jeey "2", "jeey" 3 ") trikonachya atinche samadhan karate aanee anyatha shoonya asate tevha" trikoni tribhuj "1 chya barobaricha asato. trikoni tribhuj pradeshala kadhikadhi 6-'jeey' aanee 9-'jeey' chinhanchya sadrushyat '3-' jeey 'chinh (' emm 'shivay) asey gondhalat takanare mhatale jaate, jeey serve 3-' jeey. emm. 'chinhanchi aparivartaniy berries aahet jithe konatehi chull shillak naheet.
golakar susangatateshi sambandh; gant gunank.
3-'jeey. emm.' chinhe teen golakar susangatatechya utpadanancha avibhajya bhag detat. 
sootra _ 19, sootra _ 20 aanee sootra _ 21 purnankansah. yaa samakalananna gant gunank mhanatat.
firki-bharit golakar susangatatechya samakalananshi sambandh.
sootra _ 22 asalyas firki-bharit golakar susangatatesathi samaan sambandh astitvat aaheth
asymptotic abhivyakti.
sootra _ 25 sathee shoonya nasalele 3-"jeey" chinh aahe
jethe sootra _ 27 aanee sootra _ 28 heey wigner karya aahe. samanyatah rege samamitiche palan karnyacha eka changla andaj khalilpramane deela jaatoh 
jethe sootra _ 30 aahe.
metrik tensor.
khaleel praman koneey-gatee siddhantat metrik tensor mhanoon karya karate aanee tyala 'wigner 1-jeey. emm. chinh' mhanoon dekhil olakhale jaateh
yacha vapar koneey momentavar vel ulat karnyasathi keela jaau shakato.
vishesh prakarane aanee itar malmatta.
samikaran (3.7.9) pasoon 
jethe "pii" heey dantkathetil bahupadi aahet.
raka-gunankanshi sambandh.
wigner 3-"jeey" chinhe eka sopya tappyadvare raka-gunankanshi sambandhit aaheth
gut siddhantashi sambandh.
haah vibhag moolatah paribhashit sambandhanchi punaravrutti karato
gut siddhantachya bhashet.
gatache pratinidhitva heey gatache samarupata aahe.
kahee vector jaaget resheey parivartanancha eka gut. resheey
vector jagechya kahee aadharanchya sandarbhat matrixchya gatadware parivartan dile jaau shakate.
koneey kshan eka aparivartaniy sodoon sodoon parivartanancha gut haah trimiteey firki gut aahe mhanoon (3). 
jevha "firka" koneey moment samavisht keela jaato, tevha gut haah tyacha duheri aavaran gut asato, suu (2).
qamee karata yenyajoge pratinidhitva mhanje jithe serve matricks block karn swarupat aananyasathi aadhar badal lagoo keela jaau shakato. pratinidhitva
asey konatehi parivartan astitvat naslyas teey irreducible (irrep) aahe.
jeey" chya pratyek mulyasathi, 2 "jeey" + 1 kiit heey irreducible representationsathi (irrep) aadhar tayar karatat. 
mhanoon (3)/suu (2) heey jatil sankhyanvar. done dile
erapes, tensorche thet utpadan qamee kele jaau shakate
erapeschi berries, clabsush-gorden gunankanna janm dene kinwa tiheri utpadan qamee karane 
kshullak irrep 1 chya teen irreps gatansathi chinhanna janm detat.
itar gatansathi gatansathi chinhe.
sootra _ 36 chinhacha sarvat sakhol abhyas yaa sandarbhat keela gela aahe 
koneey gatiche jodane. yasathi, tyacha drudhpane sambandh aahe
gut pratinidhitva siddhant suu (2) aanee mhanoon (3)
varr sangitalyapramane. matra, anek
bhautikshastrat itar gut mahattvache aahet aanee 
rasayanshastra,
aanee yaa itar gatansathi sootra _ 36 chinhavar barech kaam jhaale aahe.
yaa vibhagat, tyateel kahee kamancha vichar keela jaato.
fakt qamee karata yenyajoge gut.
wignercha mool kagad
(3)/suu (2) paryant maryadit navhate
parantu tyaeivaji fakt qamee karata yenyajogya (ess. aar.) gatanvar laksh kendrit kele.
heey asey gut aahet jyat
ess. aar. gatansathi, pratyek irrep tyachya jatil sanyugma samatulya aahe,
aanee stambhanchya kramparivartanankhali tyache paripoorn moolya
chinh aparivartaniy aahe aanee pratyekacha tappa nivadala jaau shakato jenekarun
teey bahudha visham kramparivartanankhali chinh badaltat aanee rahatat
summ kramparivartanankhali badal keela jaat nahee.
samanya sankshipt gut.
sankshipt gut topological sanrachanesah gatancha eka vistrut varg tayar karatat.
tyat atirikt swatantra topologies maryadit gatancha samavesh aahe.
aanee anek khote gut.
samanya sankshipt gut dvidha manahsthitit kinwa bahuvishaymukt nastil.
derome aanee tikshna
aanee deromne sootra _ 36 chinhachi tapasani kelee
samanya prakaranasathi clebsh-gorden gunankanshi sambandh vaparoon
jethe sootra _ 42 heey sootra _ 43 chya pratinidhitva jaageche pariman aahe aanee sootra _ 44 heey jatil sanyugma aahe.
sootra _ 45 chey pratinidhitva.
sootra _ 36 chinhachya stambhanchya kramparivartananche parikshan karoon tyanni teen prakarane darshavilih
yaa tattvanchya aadhare sankshipt gatansathi sootra _ 36 chinhanmadhye pudhil sanshodhan kele gele aahe.
suu (aine).
vishesh ekatmak gut suu (aine) haah nirdharak 1 saha aine × aine ekatmak matrixcha khote gut aahe.
kann siddhantat samooh suu (3) mahattvacha aahe.
sootra _ 36 kinwa tyachyashi sambandhit anek kagadpatre aahet.
samatulya chinh
samooh suu (4) sathee sootra _ 36 chinhacha abhyas keela gela aahe.
tarr samanya suu (aine) gatanvarhi kaam kele jaate
sphatikshastriy bindu gut.
maryadit sphatikshastriy bindu gatansathi sootra _ 36 chinhe kinwa clebsch-gorden gunank yanchyashi sambandhit anek kagadpatre aahet.
aanee duheri guna gut
butlerche pustak
hyancha sandarbh ghya aanee sarnyansah siddhantacha tapasheel dya.
chumbakeey gut.
chumbakeey gatanmadhye antilinear operator tasech resheey operatorcha samavesh hoto. tyancha vapar karane aavashyak aahe
ekatmak aanee ekvirodhi gatanchya mukhya sadarikaranancha wignercha siddhant.
manak pratinidhitva siddhantapasun eka lakshaniy vegalepana mhanje irreducible coor presentation sootra _ 44 chee bahulata
irreducible coor presentation sootra _ 63 chya thet utpadanat
sadharanpane tiherimadhil kshullak coor prastutikaranachya bahuvidhepeksha lahan asate
utpadan sootra _ 64, jyamule clebsch-gordenmadhye lakshaniy farak hoto
gunank aanee sootra _ 36 chinh.
rakhadi gatansathi sootra _ 36 chinhe tapasali gelee aahet.
aanee chumbakeey bindu gatansathi

