
morrie-zwanzig aupcharikta

bhautikshastradnya hejim morrie aanee robbert zwanzig yanchya navavarun morrie-zwanzig aupcharikta hii sankhyikeey bhautikshastrachi eka paddhat aahe. heey projection operatorscha vapar karoon pranalichya gatishilateche sambandhit aanee aprasangik bhagat vibhajan karnyas anumati dete, jyamule sambandhit bhagasathi gatichi bund samikarane shodhanyat madat hote. yacha vapar keela jaato eae.jee. drav yantriki kinwa ghanroop padarth bhautikshastra.
kalpana.
mothya sankhyene microscopic degree auph friedam asalelya macroscopic pranalinche varnan sahasa thodya pramanat sambandhit chalandware kele jaate, udaharanarth firkichya pranalitil chumbakatva. morrie-zwanzig aupcharikta hii sthool samikarane shodhanyas anumati dete jee keval pranalichya gatichya sookshm samikarananvar aadharit sambandhit chalanvar avalambun asatat, jee samanyatah hamiltniandware nirdharit kelee jaatat. samikarananmadhye aprasangik bhag aavaj mhanoon disato. aupcharikta sambandhit chull kaay aahet heey nirdharit karat nahee, heey samanyatah pranalichya gunadharmanmadhun prapt kele jaau shakatat.
pranaliche varnan karnare nirikshan karnyayogya padarth hilbert space tayar karatat. tyanantar prakshepan chalak sambandhit chalandware pasarlelya upkshetravar gatishilata prakshepit karato. gatishilatecha aprasangik bhag nantar sambandhit chalanchya orthogonal asalelya nirikshan karnyayogya vastunvar avalambun asato. parasparsambandh karya scalar utpadan mhanoon vaparale jaate, mhanunach aupchariktecha vapar parasparsambandh karyanchya gatishilateche vishleshan karnyasathi dekhil keela jaau shakato.
vyutpatti.
spashtapane velevar avalambun nasalele nirikshanyogya sootra _ 1 heey gatichya heisenberg samikaranache palan karate
jethe leoville operator sootra _ 3 heey quantum prakaranat commutator sootra _ 4 vaparoon aanee shastriy prakaranat poison brackett sootra _ 5 vaparoon paribhashit kele jaate. aapan yethe asey gruheet dharato qee hamiltonianmadhye spasht velevar avalambun nahee. vyutpattiche samanyikaran velevar avalambun asalelya hamiltonian lokansathi dekhil kele jaau shakate. heey samikaran aupcharikpane sodavale jaate
nirikshanyogya sootra _ 7 varr karya karnara prakshepan operator ashee paribhashit kelee jaate
jethe sootra _ 1 heey sambandhit chull aahe (jeey vividh nirikshaniy vastunche vahak dekhil asoo shakate) aanee sootra _ 10 heey prachalakanche kahee scalar utpadan aahe. samanya parasparsambandhachya karyache samanyikaran asalele 'morrie' utpadan samanyatah yaa scalar utpadanasathi vaparale jaate. nirikshanksham sootra _ 11 sathee, tyachi vyakhya ashee kelee jaateh
jethe sootra _ 13 heey vyutkram tapman aahe, tethe trace (shastriy prakaranat fages spaceveril avibhajya bhagashi sambandhit) aanee sootra _ 14 heey hamiltonian aahe. sootra _ 15 heey sambandhit sambhavyata prachalak (kinwa quantum pranalinsathi ghanata prachalak) aahe. heey asha prakare nivadle jaate qee teey keval sambandhit chalanche karya mhanoon lihile jaau shakate, parantu vastavik ghanatesathi eka changla andaj aahe, visheshtah jenekarun teey yogya sarasari moolye deil.
aata aapan operatorchi olakh lagoo karato.
teey
varr sadar kelela prakshepan chalak aanee vyakhya vaparoon
(frequency matricks),
(yadruchchik shakti) aanee
(smrutee karya), parinam asey lihile jaau shakate
heey nirikshanyogya sootra _ 22 sathee gatiche samikaran aahe, jeey sadhyachya velechya sootra _ 23 madheel tyachya mulyavar, mageel veleteel mulyavar (smrutee sandnya) aanee yadruchchik shaktivar (aavaj, gatishilatechya bhagavar avalambun asato joou sootra _ 24 chya orthogonal aahe) avalambun asate.
markovian andaj.
varr dilele samikaran samanyatah convolution termmule sodavane katheen asate. aaplyala samanyatah sookshm dhvanipeksha khoop mothe velman badalana santh sthool chalanmadhye swarasya asalyane, yacha parinam convolutionmadhil vilambakade durlaksh kartana anant velechya maryadevar samakalit honyacha hoto. heey samikaran sootra _ 25 madhye dusya kramane vistaroon aapan pahato,
kuthe?
samanyikaran.
thermodynamic samatolapasun mothya vichalanansathi, morrie-zwanzig aupcharikteche adhik samanya swaroop vaparale jaate, jyatoon mageel parinam reshatmakatedvare prapt kele jaau shakatat. yaa prakaranat, hamiltonianche spasht vel-avalambitva aahe. yaa prakaranat, chalasathiche vahtook samikaran
jethe sootra _ 29 heey sarasari moolya aahe aanee sootra _ 30 heey chadh-utaar aahe, asey lihile pahije (punaravrutti kelelya nirdeshankanvar berijsah nirdeshank sanketan vapara)
kuthe?
aanee
aapan vel-krambaddha ghatankiy vaparale aahe
aanee velevar avalambun asalela prakshepan chalak
hii samikarane morrie utpadanache samanyikaran vaparoon punha lihili jaau shakatat. velevar avalambun asalelya hamiltonian aanee aniyantrit gatishil pranalinvar aupcharikta lagoo karnyasathi pudhil samanyikaranancha vapar keela jaau shakato.