
satatyamadhye baddh sthitee

satatyatil (bii. aay. see.) baddh sthitee hii kahee vishisht quantum pranalichi eigen sthitee aahe jyat khaleel gunadharm aaheth
electronic, photonic, dhwanik pranalinmadhye dvigunit aadhaltat. nishiddha kshetramadhye, jethe anantatevar konatehi maryadit upay nasatat, tyaa bandhit avastha vyapakpane dnyat aahet (anoo, quantum thipke, ardhvahakanmadhil dosh). yaa satatyashi sambandhit asalelya satatyatil dravanansathi, anunad avasthe dnyat aahet, jyaa kalantarane kshay hotat (urja gamavatat). udaharanarth, tyach urjechya aapatkalin laharimule teey uttejit houu shakatat. satatyatil baddh avasthanmadhye vastavik urja eigenvalues asatat aanee mhanoon teey nirantar varnpatatil avasthanshi parasparkriya karat naheet aanee kshay karoo shakat naheet.
wigner-vonn neuman bicks.
yujeen wigner aanee johnn wonn neuman yanni 1929 madhye satatyatil baddh avasthancha pratham andaj vartavala hota. done sambhavyateche varnan kele gele hote, jyamadhye dvigun done vegvegalya karanansathi disatat.
yaa karyat, golakar samamiteey tarang karya pratham nivadle jaate jenekarun sampoorn jaaget chaturthansh samakalit kele jaau shakel. mug eka kshamata ashee nivadali jaate qee heey wave function shoonya urjeshi sambandhit asel.
sambhavya golakar samamiteey aahe, mug lahariche samikaran khalilpramane lihile jailah
konache vyutpann nahise hotat, kaaran aapan swatahla keval golakar samamiteey lahari karyancha vichar karnyapurte maryadit thevatoh
golakar samamiteey tarang karya sootra 4 sathee sootra _ 3 heey eigen moolya honyasathi, sambhavya asane aavashyak aahe
aaplyala vishisht moolye sootra _ 6 aanee sootra _ 7 midatat jyasathi bic chey nirikshan kele jaeel.
pahila prakaran.
chala function sootra _ 8 chaa vichar karuya. avibhajya sootra _ 9 maryadit asale pahije, tarr sootra _ 10 asatana vartan vicharat ghetalyas, aaplyala teey sootra _ 11 milate, nantar sootra _ 12 asatana vartan vicharat ghetalyas, aaplyala sootra _ 13 milate. sootra _ 15 madheel niyamitata sootra _ 14 laa sootra _ 16 aavashyak aahe. shevati, aaplyala sootra _ 17 milate.
sootra _ 18 gruheet dharalyas, nantar kshamata (aprasangik gunak sootra _ 19 takoon) chya barobarichi aselah
eigen function aanee sambhavya vakr aakrutimadhye darshavile aahet. asey disate qee electron fakt kshamata bund karel aanee urja ghan varnpatatil asel, parantu sootra _ 3 saha eka sthir kaksha aahe.
yaa karyat khaleel arth deela aaheh heey vartan shastriy yantrikishi asalelya sadrushyavarun samajale jaau shakate (vichar heey lio sylardshee sambandhit aahet). sambhavya sootra _ 22 madheel bhautik binduchya gatiche varnan khaleel samikaranadvare kele aaheh
heey pahane sope aahe qee jevha sootra _ 25, sootra _ 26, tevha asymptotic aahe
mhanjech, maryadit velechya sutrasathi _ 29 haah bindu anantakade jaato. sthir dravan sootra _ 30 chaa arth assa aahe qee bindu punha anantatoon parat yeto, qee too tethoon paravartit jhaala aahe aanee dolan suru karato. sootra _ 12 varr sootra _ 30 shunyakade valate hii vastusthiti, teey mothya sambhavya slidechya khalee sarakate aanee prachand veg aahe aanee mhanoon tyache ayushya qamee aahe yaa vastusthitivarun yete. aanee sampoorn dolan prakriya (sootra _ 33 teey anant aanee mage) niyatkalik asalyane, yaa quantum yantrik samasyeche sthir nirakaran asane tarkik aahe.
dusare prakaran.
chala dusya udaharanakade valooya, jyacha arth asha vicharanmadhun lavala jaau shakat nahee.
sarvapratham, aapan eka karya sootra _ 34 gheto, nantar sootra _ 35. yaa bhinn golakar lahari aahet, kaaran urja sootra _ 3 heey sambhavya sootra _ 35 peksha mothe aahe, shastriy gatij urja sakaratmak rahate. wave function heey satatchya varnapatat asate, avibhajya sootra _ 38 vegale hote. chala wave function badalanyacha prayatna karuya jenekarun quadratic integral converge hoil aanee potential-1 chya jawal badalel.
khaleel uttarancha vichar karah
jarr karya sootra _ 40 satat asel aanee sootra _ 41 varr asymptotic sootra _ 42 asel tarr avibhajya maryadit aahe. tyanantar kshamata samaan asel (mool lekhatil durust kelelya ankganitiy trutisah):
sambhavyata-1 chya jawal rahnyasathi aanee sootra _ 25 varr-1 kadey cull karnyasathi, aapan karyanche sootra _ 45 lahan aanee sootra _ 25 varr shoonyakade cull karane aavashyak aahe.
pahilya prakaranat, sootra _ 47 dekhil sootra _ 48 sathee nahise jhaale pahije, mhanje sootra _ 49 sathee, mhanje sootra _ 50 sathee. jevha sootra _ 51 kinwa yaa abhivyaktiche itar konatehi karya asate tevha asey hote.
sootra _ 52 gruheet dharuya, jethe sootra _ 53 aniyantrit aahe (yethe sootra _ 40 sootra _ 25 asatana sootra _ 42 kadey valate). mug
sambhavyatesathiche samikaran avghad aahe, parantu aalekh darshavtat qee sootra _ 25 sathee sambhavyatecha cull-1 asato.
yavyatirikt, asey disun yete qee konatyahi sutrasathi _ 59 assa 'aaa' nivadu shakato qee potential sootra _ 60 aanee sootra _ 61 darmyan asel.
aapan pahoo shakato qee potential _ 62 yaa kalavadhichya sutrasah dolan karate aanee wave function _ 63 yaa kalavadhichya sutrasah dolan karate. asey disun yete qee asha potentialchya "humps" madheel serve paravartit lahari tappyamadhye aahet aanee function madhyabhagi sthanbaddh kele jaate, jeey bregg mirarchya paravartanasarkhya yantranedvare potentialmadhun paravartit hote.