
prasaar monte carlo

prasaar monte carlo (dee. aim. see.) yaa prasaar quantum monte carlo ack quantum monte carlo vidhi haye joe schroedinger sameekaran koo hull karane key liye ack harey rung key kaary kaa upayog karati haye. dee. aim. see. sambhaavit roop seey sankhyaatmak roop seey sateek haye, jiska arth haye kii yeh kissy bhee quantum pranali key liye dee gaee truti key bheetar sateek bhoo-avastha oorjaa kaa pataa lagaa sakata haye. jaba vaastav mein ganana kaa prayaas kiya jaataa haye, tou koee yeh paataa haye kii bosans key liye, algorithm system key aakar key saath ack bahupad key roop mein, lekin fermian key liye, system key aakar key saath teji seey dee. aim. see. scale kartaa haye. yeh fermian key liye sateek badey paimaane parr dee. aim. see. anukaran koo asambhav banaata haye; haalaanki, nishchit-node sanniktan key roop mein jaane jaane vaale ack chatur sanniktan koo niyojit karane vaale dee. aim. see. abhee bhee bahut sateek parinam dey sakate hain.
projector vidhi.
algorithm koo prerit karane key liye, aaie ack ayam mein kuchh kshamata mein ack kann key liye schroedinger sameekaran koo dekhein. 
humm ack "prachaalak" sameekaran key sandarbh mein likh curr sanketan koo thodaa sanghanit curr sakate hain, 
tou phir humm 
jahan hamein yeh dhyaan rakhna hoga kii sootra _ 4 ack prachaalak haye, naa kii ack saral sankhya yaa kaary. vishesh kaary hain, jinhen eigenfunctions kahaa jaataa haye, jisake liye sootra _ 5, jahan sootra _ 6 ack sankhya haye. yeye kaary vishesh hain kyonki koee fark naheen padata kii humm tarang falan parr sootra _ 4 operator kii kriya kaa mulyankan karate hain, hamein hamesha ack hii sankhya sootra _ 6 milata haye. inn karyon koo sthir avastha kahaa jaataa haye, kyonki kissy bhee bindu sootra _ 9 parr samay vyutpann hamesha samaan hotaa haye, isaliye tarang falan kaa ayam samay mein kabhi naheen badalata haye. choonki ack tarang falan kaa samagr charan maapane yogya naheen haye, isaliye pranali samay key saath naheen badalati haye.
humm aamtaur parr sabse cumm oorjaa igenvalue, ground state key saath tarang kaary mein ruchi rakhate hain. humm schroedinger sameekaran kaa thodaa alag sanskaran likhane jaa rahey hain jisamen samaan oorjaa igenvalue hoga, lekin, ausilator honey key bajaay, yeh abhisari hoga. yahaan yeh haih
hamane samay vyutpann seey kaalpanik sankhya koo hataa diyaa haye aur sootra _ 11 key sthir offset mein jodaa haye, joe kii bhoo-avastha oorjaa haye. humm vaastav mein jamini sthiti oorjaa koo naheen jaanate hain, lekin ise swa-nirantarta seey nirdhaarit karane kaa ack tarika hoga jise humm baad mein pesh karenge. hamaare sanshodhit sameekaran (kuchh loga ise kaalpanik-samay schroedinger sameekaran kahate hain) mein kuchh achche guna hain. pahali baat yeh haye kii yadi humm ground state wave function kaa anuman lagaate hain, tou sootra _ 12 aur samay vyutpann shoonya haye. abb maan leejiye kii humm ack aur tarang falan (sootra _ 13) seey shuru karate hain, joe jamini sthiti naheen haye lekin isake liye orthogonal naheen haye. taba humm ise eigenfunctions key raikhik yog key roop mein likh sakate hainh
choonki yeh ack raikhik avkal sameekaran haye, isaliye humm pratyek bhaag kii kriya koo alag seey dekh sakate hain. humm pahale seey hii nirdhaarit curr chuke hain kii sootra _ 15 sthir haye. maan leejiye kii humm sootra 16 lete hain. kyonki sootra 15 sabse cumm oorjaa vaalaa igen function haye, sootra 16 kaa sahayogi igenvalue guna sootra 19 koo santusht kartaa haye. iss prakaar sootra 20 kaa samay vyutpann nakaratmak haye, aur antatah shoonya parr jaayega, jisase hamein kewal jamini sthiti key saath chhod diyaa jaayega. yeh avalokan hamein sootra _ 11 nirdhaarit karane kaa ack tarika bhee detaa haye. humm samay key madhyam seey prasaar karate hue tarang falan key ayam koo dekhate hain. yadi yeh badhata haye, tou offset oorjaa key anuman koo cumm karein. yadi ayam cumm hoe jaataa haye, tou offset oorjaa kaa anuman badhaaen.
yaadrichhik karyanvayan.
abb hamaare paas ack sameekaran haye kii, jaise-jaise humm ise samay parr aage badhaate hain aur sootra _ 11 koo uchit roop seey samaayojit karate hain, humm paate hain kii
kissy bhee diye gaye hamiltonian kii jamini sthiti. yeh abhee bhee shaastriya yantriki kii tulanaa mein ack kathin samasya haye, halanki, kyonki isake bajaay 
kanon kii ekal sthiti kaa prachaar karate hue, hamein poore karyon kaa prachaar karna chaahiye. shaastriya yantriki mein, humm anukaran curr sakate hain
sootra _ 23 nirdhaarit karke kanon kii gati, yadi humm maan lein kii bull sootra _ 24 key samay avadhi mein sthir haye. kaalpanik samay schroedinger sameekaran key liye, isake bajaay, humm ack vishesh kaary key saath ack convolution integral kaa upayog karke samay mein aage badhate hain jise green function kahaa jaataa haye. tou hamein sootra _ 25 milata haye. isi tarah shaastriya yantriki key liye, humm kewal samay key chhote tukadon key liye prachaar curr sakate hain; anyatha harey rung kaa kaary galat haye. jaise-jaise kanon kii sankhya badhati haye, samakalan kii ayamita bhee badhati haye, kyonki hamein sabhi kanon key sabhi nirdeshankon parr ekikrit karna hotaa haye. humm inn samakalanon koo monte carlo samakalan dwara curr sakate hain.

