
shriefer-wolf parivartan

quantum yantrikimadhye, shriefer-wolf parivartan heey eka ekatmak parivartan aahe jeey parasparsanvadat hamiltonian pranalila pahilya kramane vikarn karnyasathi vaparale jaate. tyamule, shriefer-wolf parivartan hii dusya kramankachya vikshobh siddhantachi eka prachalak aavrutti aahe. qamee urjeche prabhavi model midvinyasathi dilelya anek-shareer hamiltonianchya uchch urja uttejana prakshepit karnyasathi scriffer-wolf parivartan anekada vaparale jaate. asha prakare, schreifer-wolf parivartan heey quantum-anek shareer hamiltonianchya majboot jodani vyavasthecha abhyas karnyasathi eka niyantrit ashant marg pradan karate.
jaree samanyatah jeey. yanni anderson ashuddhata modelmadhun kondo model midavalelya kagdala shrey dile aahe.aar. shriefer aanee pii.aaa. wolf.jockwin mazdak luttinger aanee walter kohan yanni hii paddhat naun-periodic kepi perterbation thiaribaddalachya aadhichya karyat vaparali. shriefer-wolf parivartan vaparoon, anderson ashuddhata modelmadhye upasthit asalelya uchch urja shulk uttejanacha andaj lavala jaato aanee qamee urja prabhavi hamiltonian prapt keela jaato jyamadhye keval aabhasi shulk chadhautar asatat. anderson ashuddhata model prakaranasathi, shriefer-wolf parivartanane darshavile qee kondo model anderson ashuddhata modelchya majboot jodani vyavasthet aahe.
vyutpatti.
formchya time-independent hamiltonian operator formula _ 1 antargat vikasit honanya quantum pranalicha vichar karah formula _ 2 jethe formula _ 3 heey dnyat eigenstate formula _ 4 aanee sambandhit eigenvalues formula _ 5 saha hamiltonian aahe aanee jethe formula _ 6 eka lahan vikshobh aahe. shivay, sarvasadharanata naan gamavata asey gruheet dharale jaate qee sootra _ 3, i chya eigenbesismadhye sootra _ 6 heey purnapane auph-diagonal aahe.eae., serve sutransathi sootra _ 9. kharokhar, hii paristhiti nehmi sootra _ 6 chya karn ghatakanna sootra _ 3 madhye shoshun gheuun, asha prakare tyachi eigenvalues formula _ 13 madhye sudharit karoon vyavasthit kelee jaau shakate.
shriffer-wolf parivartan heey eka ekatmak parivartan aahe jeey hamiltonianla eka aadharavar ('dressed' besis) vyakt karate jithe teey vikshobh sootra _ 6 madhye pahilya kramane karn aahe. heey ekatmak parivartan paramparikpane asey lihile jaateh sootra _ 15 jevha sootra _ 6 lahan asate, tevha parivartanache generator sootra _ 17 dekhil titkech lahan asel. tyanantar bekar-campbelle-hasdorf sutrasutra _ 19 vaparoon formulamadhye parivartan vadhavale jaau shakate, yethe formula _ 20 heey operator formula _ 21 aanee formula _ 22 madheel commutator aahe. formula _ 3 aanee formula _ 6 chya drushtine, parivartan formula _ 25 banate, hamiltonianla generator formula _ 17 asha formula _ 28 nivadoon formula _ 6 madhye pahilya kramane vikarn kele jaau shakate, yaa samikaranala nehmi eka nishchit upay asato, yaa gruhitkanusar qee formula _ 6 heey formula _ 3 chya eigenbesismadhye vikarn nahee. mageel parivartan utpannamadhye hii nivad badalaneh formula _ 31 hii abhivyakti schreifer-volf parivartanache manak swaroop aahe. lakshat ghya qee ujavya bajuche serve operator aata pahilya kramashi parasparsanvad sootra _ 6 dware 'dressed' yaa naveen aadharavar vyakt kele jaatat.
sarvasadharanpane, parivartanachi katheen payari mhanje generator sutrasathi spasht abhivyakti shodhane. heey ekada kele qee, commutator sootra _ 34 mojoon shriefer-wolf hamiltonianchi ganana karane sope aahe. tyanantar hamiltonianla tyaa upkshetrasathi prabhavi prakshepit hamiltonian midvinyasathi swarasya asalelya konatyahi upkshetravar prakshepit kele jaau shakate. parivartan achook honyasathi, kadhoon takaleli upasthanke swarasya asalelya upasthanapasun urjavanpane changli vegali asane aavashyak aahe, mhanje parasparsanvad sootra _ 6 chee takad upasthananmadhil urja farkapeksha khoopach qamee asane aavashyak aahe. hii praman dviteey-kram vikshobh siddhantatil vaidhatechi teech vyavastha aahe.
vishisht prakaran.
block-diagonal asalelya abadhit hamiltonianchya vishisht prakaranat, schriefer-wolf (ess. doubleu.) parivartanachi pratyaksh ganana kashee karayachi heey haah vibhag spasht karel. 
parantu pratham, konatyahi goshtichi yogya ganana karnyasathi, sampoorn prakriyedarmyan pratyakshat kaay ghadat aahe heey samajoon ghene mahatvache aahe. swa. parivartan sootra _ 36 eksandh asalyane, teey mahitiche praman kinwa hamiltonianchi jatilata badalat nahee. matra, matricks ghatakanchya parinami honanya badalamule mahitimadhye eka padanukram tayar hoto (udaa.jee. eigenvalues), jeey nantar sambandhit kshetratil prakshepanasathi vaparale jaau shakate. yavyatirikt, jevha khand jodanare karnabahya ghatak vishisht vikshipt urja pramananpeksha khoopach lahan asatat, tevha samasya sulabh karnyasathi vikshipt vistaras parvanagi dilee jaate.
aata, thosatesathi, bhautikshastrat swatantra blocks sootra _ 39 pasoon banavalelya akhand bhag sutrasah purn hamiltonian sootra _ 37 chaa vichar qaraa aanee swa parivartanachya mool prernemadhye, pratyek block eka vegalya urja pramananshi sambandhit asane apekshit aahe. visheshtah, serve ksheen urjechi patali ekach khandachi asali pahije. heey changle vibhajan jhalele hamiltonian heey aapale prarambhik bindu sootra aahe. eka vikshipt jodani sootra _ 6 aata eka vishisht arthavar gheteh vegvegalya kshetranna jodanara vishisht matricks ghatak tyaa kshetranmadhil eigenvalue farkanpeksha khoopach lahan asane aavashyak aahe. ess. doubleu. parivartan pratyek block sootra _ 39 laa prabhavi hamiltonian sootra _ 43 madhye sudharit karel, jyamadhye vikshobh sootra _ 6 dware itar blocksche parinam samavisht kele jaatil ("integrating out"). shevati, vyaj kshetrakade (jyala prakshepan mhanatat) pahane aanee udaharanarth, eigenvalues aanee igenvectorschi ganana karnyasathi nivadalelya prabhavi hamiltonians kaam karane purese aahe. bhautikshastrat, yamule prabhavi qamee (kinwa uchch) urja hamiltonian tayar hotil.
mageel vibhagat namood kelyapramane, katheen payari mhanje ess. doubleu. parivartanachya generator sootra _ 17 chee ganana karane. dusya kramankachya vikshobh siddhantashi tulana karata yenyajoge parinam midvinyasathi, samikaran sootra _ 46 sodavane purese aahe (vyutpatti pahaa). jevha sootra _ 3 heey khand-karn asate tevha done payyanmadhye eka sopee yukti upalabdh asate.
pahilya tappyat ekatmak parivartan sootra _ 48 vikarn sootra _ 3 shodhane samavisht aahe. pratyek block sootra _ 39 heey ekatmak parivartan sootra _ 51 saha vikarn kele jaau shakate (heey sootra _ 39 chya ujavya-igenvectors matricks aahe), heey sootra _ 53 tayar karnyasathi purese aahe, jeey tyachya vikarnavar lahan paribhraman sootra _ 51 neey banalele aahe, sootra _ 3 chey purnapane vikarn matricks sootra _ 56 madhye rupantar karnyasathi. 
sampoorn matricks sutravar _ 48 sutracha vapar kelyas _ 1 utpann milate
sootra _ 59
rupantarit vikshobh sutrasah _ 60, jeey tiryak rahate. yaa naveen swarupat, sootra _ 17 mojanyachi dusari payari khoop sopee hote, kaaran aaplyala ghatakanmadhye eka spasht abhivyakti milateh
sootra _ 62
jethe sootra _ 63 heey sootra _ 65 chya karnavaril sootra _ 64 vaa ghatak darshavite. yache kaaran heey nirikshanatun yete qee, konatyahi matricks sootra _ 66 aanee karn matricks sootra _ 67 sathee, aaplyakade sambandh sootra _ 68 aahe. sootra _ 69 sathee generator sootra _ 70 dware paribhashit kele jaat asalyane, vareel sootra lagech anusaran karate. apekshepramane, sambandhit prachalak sootra _ 71 ekatmak aahe (teey sootra _ 72 chey samadhan karate) kaaran sootra _ 17 chaa chhed jevha sthanantarit hoto tevha chinh badalato aanee sootra _ 6 heey hermician aahe.
vyutpattitil shevatche sootra vaparoon, dusya kramankache schreifer-wolf-rupantarit hamiltonian sootra _ 75 aata tyachya prathamik sandnyanche sootra _ 65 aanee sootra _ 77 chey karya mhanoon eka spasht swaroop aaheh
sootra _ 78
paridhan kelelya' rajyanmadhye urja asate
sootra _ 79
pratham-kram (gair-vighatan) vikshobh siddhantachya pakakrutiche anusaran karane. heey lagoo hote kaaran swa parivartan heey andaje sootra 80 varr aadharit aahe, lakshat ghya qee ekatmak paribhraman sootra 48 haah eigenvaluesvar parinam karat nahee, mhanje sootra _ 82 heey mool hamiltonian sootra _ 1 sathee dekhil eka arthpurn andaj aahe.
pratham-kramatil vikshobh siddhantatahi, 'paridhan keleli' sthitee swatah vyutpann kelee jaau shakate, jase qee
sootra _ 84
sootra 69 chaa vartaman firalela aadhar lakshat ghenyasathi sootra 65 chya abadhit eigenstate sootra 86 chey nirdeshank sootra _ 85 kadey laksh dya. sootra 1 chya naisargik aadhar sootra 89 madhye eigenstate vyakt karnyasathi, ekatmak parivartan sootra _ 91 karane aavashyak aahe.