
laflin wavefunction

ghanroop padarth bhautikshastrat, loglin wavefunction heey eka ansatz aahe, jeey robbert laflinne prastavit kele aahe, jeey eksaman gelium parshvabhoomichya parshvabhumivar eksaman parshvabhoomi chumbakeey kshetrat thevalelya dvimiteey electron vayuchya jaminichya sthitisathi jevha sarvat qamee landau patalicha bharane ghatak (quantum holl effect) sootra 1 asato, jethe sootra 2 haah visham sakaratmak purnank asato. heey _ 3 fractional quantum holl effect yaa sootrachya nirikshanala spasht karnyasathi bandhanyat aale hote aanee atirikt sootra _ 4 avasthanchya astitvacha tasech fractional vidyut charge sootra _ 5 saha ardh-kananchya utsahacha andaj vartavanyat aala hota, jeey donhi nantar prayogikdrushtya nirikshanat aale. yaa shodhasathi laflinla 1998 madhye bhautikshastratil nobel puraskaracha eka trutiyansh puraskar midala. chachani tarang karya asalyane, teey achook nahee, parantu gunatmakdrushtya, teey achook samadhanachi anek vaishishtye punarutpadit karate aanee parimanatmakdrushtya, lahan pranalinsathi achook ground states tyache khoop jaast overlap aahe.
jarr aapan shoonya kramache andaje mhanoon electronmadhil gelium aanee paraspar kulamb pratikarshanakade durlaksh kele, tarr aaplyakade anantapane ksheen jhaleli sarvat qamee landau patali (ell. ell. ell.) aahe aanee 1/aine. bharnyachya ghatkashi, aapan apeksha karoo qee serve electron ell. ell. ell. madhye asateel. parasparsanvad chaloo kelyavar, serve electron lll madhye aahet yacha andaj aapan lavu shakato. jarr sootra _ 6 heey sarvat qamee kakshiy koneey momentas lll sthitiche ekal kann tarang karya asel, tarr bahu kann tarang karyasathi laflin ansatz aahe
jethe sthitee darshavili jaate
inn (gossian units)
aanee sootra _ 10 aanee sootra _ 11 heey xy pratalatil nirdeshank aahet. yethe sootra _ 12 heey qamee jhalelya plankcha sthirank aahe, sootra _ 13 heey electron charge aahe, sootra _ 14 hii kananchi ekoon sankhya aahe aanee sootra _ 15 heey chumbakeey kshetra aahe, jeey xy pratalala lumb aahe. zedvaril abhilikhit akshar heey kann olakhatat. fermiansche varnan karnyasathi vevfunctionsathi, n haah visham purnank asane aavashyak aahe. yamule kananchya adalabadlantargat tarangprakriya pratisamitiy honyas bhag padate. yaa sthitisathi koneey gatee sootra _ 16 aahe.
done kanansathi parasparsanvadachi urja.
lodgelyn wavefunction heey ardhakanansathiche bahu-kann wavefunction aahe. ardhakananchya jodisathi parasparsanvad urjeche apekshit moolya aahe 
jethe padtalleli kshamata aahe (chumbakeey kshetrat antarbhut asalelya done vidyutpravah loopmadhil cullomb kshamata pahaa)
jethe sootra _ 19 heey eka sammishra hypergiometric karya aahe aanee sootra _ 20 heey pahilya prakarche besal karya aahe. yethe, sootra _ 21 heey done vidyutpravah loopchya kendranmadhil antar aahe, sootra _ 22 heey electron chargeche pariman aahe, sootra _ 23 hii larmer trijyechi quantum aavrutti aahe aanee sootra _ 24 hii chumbakeey kshetrachya dishene electron vayuchi jaadi aahe. done swatantra vidyutpravah loopche koneey moment sootra _ 25 aanee sootra _ 26 aahet jethe sootra _ 27. ulat tapasanichi lambi (gossian units) dware dilee jaate.
jethe sootra _ 29 heey cyclotron frequency aahe aanee sootra _ 30 heey xy pratalatil electron vayuche kshetrafal aahe.
parasparsanvad urjeche moolyankan asey kele jaateh
haah parinam prapt karnyasathi aapan integration variablesmadhye badal keela aahe. 
aanee
aanee nondavale (quantum kshetra siddhantatil samanya samakalan pahaa)
parasparsanvad urjesathi kiman urja aahe (aakruti 1)
aanee 
koneey momentchya gunottaratil yaa mulyansathi, urja aakruti 2 madhye sootra _ 38 chey karya mhanoon rekhatali aahe.