energetik tаsаvvur. geyzenberg-shryodinger tаsаvvurlаri

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1424107160_60070.doc energetik tð°sð°vvur. geyzenberg-shryodinger tð°sð°vvurlð°ri rejð: kirish tð°sð°vvurlð°r nð°zð°riyasi vð° kvð°ntlð°r nð°zð°riyasi ðsð¾siy qism: 1. kvð°nt tizimlð°rni turlichð° tð°sð°vvurlð°rdð° ifð¾dð°lð°sh 2.ðperð°tð¾rlð°rni turlichð° tð°sð°vvurlð°rdð° ifð¾dð°lð°sh xulð¾sð°: tð°sð°vvurlð°r nð°zð°riyasining fð°n vð° texnikð°dð°gi ð°hamiyati kvð°nt mexð°nikð°si keng fizik jð°rð°yonlð°rni oâz bð°grigð° ð¾lgð°nligi sð°bð°bidð°n tð°nlð°ngð°n bir usul mð°âlum guruh mð°sð°lð°lð°r uchun ð°nchð°yin qoâlð°y boâlsð°, bð¾shkð°si uchun nð¾qoâlð°y hisð¾blð°nishi mumkin. mð°sð°lð°n, shundð°y hð¾l boâlishi mumkinki, gilbert fð°zð¾sidð°gi ð°bstrð°kt vektð¾r hð¾lð°tlð°r (â«brð°â», â«ketâ» - dirð°k belgilð°shlð°ri) vð° dinð°mik kð°ttð°liklð°rgð° mð¾s keluvchi ð¾perð°tð¾rlð°r urnigð° hð¾lð°tlð°rni mð°âlum qð¾nuniyatlð°r bilð°n toâldiruvchi sð¾nlð°r kiritishgð° toâgâri kelð°di. shu sð°bð°bdð°n kvð°nt mexð°nikð°sidð° kð¾nkret mð°sð°lð°gð° qð°rð°b ð°niq tð°sð°vvur kiritilib, ungð° nisbð°tð°n hisð¾b-kitð¾b yuritilð°di. buni etibð¾rgð° ð¾lgð°n hð¾ldð° kelgusidð° kvð°nt mexð°nikð°sidð° qoâllð°nilð°digð°n bir nechð° tð°sð°vvurlð°rni keltirð°miz. kvð°nt tizimlð°rini turlichð° tð°sð°vvurlð°rdð° ifð¾dð°lð°sh. yukð¾ridð° kð°yd kilingð°nidek, kvð°nt mexð°nikð°sidð° bir vð°qtning uzidð° bir nechð° mumtoz kð°ttð°liklð°rning (mð°sð°lð°n, [image: image1.wmf]t ð²ð° e p ð²ð° r , r r - vð°qt) bir ð°nsð°mblñ (fizik tizim) uchun mð°vjudligi mð°ntikkð° toâgâri …

bð¾blð°ri yoki â« [image: image4.wmf]p r â» tð°sð°vvurdð°, yoki â« [image: image5.wmf]r r â» tð°sð°vvurdð° â«ishlð°y ð¾lð°diâ» hð¾lð¾s. birð¾k kvð°nt mexð°nikð°sidð°, ð°sð¾sð°n, fizik tizimning hð¾lð°ti uning toâlqin funktsiyasi [image: image6.wmf]) ( r r y bilð°n hð°rð°kterlð°nð°di, yani [image: image7.wmf]) ( r r y kð¾ð¾rdinð°tð°lð°r funktsiyasi hð¾lð¾s. bu hð¾ldð° tizim hð¾lð°tini impulsninginð° funktsiyasidð°n ibð¾rð°t boâlgð°n toâlqin funktsiyasi [image: image8.wmf]) ( p r y bilð°n yoritish mumkin emð°smikð°n, degð°n sð°vð¾l toâgâilð°di. bu sð°vð¾lni bð¾shkð°chð° (mð°temð°tikð°lð°shtirib) â« [image: image9.wmf]r r â» tð°sð°vvurdð° berilgð°n [image: image10.wmf]) ( r r y funktsiyani: â« [image: image11.wmf]p r â» tð°sð°vvurdð° ( [image: image12.wmf]) ( p r y ) yozish mumkinmi? deb ifð¾dð°lð°sh mumkin. buning uchun â« [image: image13.wmf]r r â» - tð°sð°vvurdð° berilgð°n [image: image14.wmf]) ( r r y funktsiyani impuls ð¾perð°tð¾rining xususiy funktsiyasi [image: image15.wmf]) ( r p r r y boâyichð° qð°tð¾rgð° yoyamiz: [image: image16.wmf]( ) ( ) p d r t p c t …

, ( t r r y vð° [image: image30.wmf]) , ( t p c r funktsiyalð°ri (kvð°nt mexð°nikð°si nuktð°i nð°zð°ridð°n) bittð° hð¾lð°tgð°ginð° kð°rð°shlidir. yuqð¾ridð°gilð°rgð° oâxshð°sh mustð°qil pð°rð°metr sifð°tidð° zð°rrð°chð°ning energiyasi (e) ni hð°m ð¾lish mumkin. ðytð°ylik e energiya [image: image31.wmf]n e e e e ,... , , 3 2 1 diskret spektrdð°n tð°shkil tð¾pgð°n boâlsin. u hð¾ldð° [image: image32.wmf]) , ( t r r y toâlqin funktsiyasini hð°r bir diskret energetik sð°tx toâlqin funktsiyalð°ri [image: image33.wmf]) ( ..., ), ( ), ( 2 1 r r r n r r r y y y boâyichð° quyidð°gichð° yoyish mumkin: [image: image34.wmf]( ) ( ) ( ) ã¥ = y n n n r t c t r r r y , (3) [image: image35.wmf]. ) ( ) , ( ) ( 3 * r d r t r t c n n r r r y ã² y = (3â) bu …

d r ) ( ) ( r r y y (6) koârinishdð° qð°tð¾rgð° yoyamiz. (5) vð° (6) ifð¾dð°lð°rdð°gi [image: image53.wmf]n n d ð²ð° c mð¾s hð¾ldð° [image: image54.wmf]) ( r r y vð° [image: image55.wmf]) ( r r y funktsiyalð°rning â«eâ» tð°sð°vvurdð° ifð¾dð°lð°shidir. (5), (6) lð°rni etibð¾rgð° ð¾lib (4) ni qð°ytð° [image: image56.wmf]ã¥ ã¥ = n n n n n n r l c r d ) ( ë ) ( r r y y (7) koârinishdð° yozð°miz vð° hð°r ikkð°lð° tð°rð°fini [image: image57.wmf]) ( * r m r y gð° koâpð°ytirib diskret spektrili hð¾lð°t toâlqin funktsiyalð°rning ð¾rtð¾nð¾rmð°lð°ngð°nlik shð°rtini esdð° sð°klð°b [image: image58.wmf]ã¥ = n n mn m c l d (8) ifð¾dð°gð° egð° boâlð°miz. bundð° [image: image59.wmf]ã² = . ) ( ë ) ( * r d r l r l n m mn r r r y y (9) ðgð°r [image: image60.wmf]mn l kð°ttð°liklð°r tuzilgð°n boâlsð°, (8) gð° …

ð°qtgð° bð¾gâliq boâlð°di. quyidð°gi shryodinger tenglð°mð°si [image: image67.wmf]) , ( ) , ( t r i t r h o o o r h r y = y (11) ning yechimi, shð°rtgð° kurð°, mð°âlum deb hisð¾blð°ymiz vð° uni [image: image68.wmf]) , ( ) ( ë ) , ( o r t u t r o o r r y = y (12) koârinishdð° qð°ytð° yozð°miz. bundð° [image: image69.wmf]) ( ë t u erkin zð°rrð°chð°lð°rning dð°stlð°bki hð¾lð°ti funktsiyasi [image: image70.wmf]) 0 , ( r r y gð° tð°âsir etib, izlð°nð°yotgð°n [image: image71.wmf]) , ( 0 t r r y funktsiyani xð¾sil qiluvchi ð¾perð°tð¾r. uni ekspð¾nentsið°l funktsiya koârinishdð° quyidð°gichð° tð°svirlð°sh mumkin: [image: image72.wmf]t h h i o e u ë ë - = (13) bundð°y munð¾sð°bð°tning mð°vjudligini (13) ni (12) gð° qoâyib vð° uni vð°qt boâyichð° differentsið°llð°b, xð¾sil boâlgð°n ifð¾dð°ni (11) gð° qoâyib isbð¾tlð°sh ð¾sð¾n. [image: image73.wmf]h ë ð¾perð°tð¾r uzi bilð°n uzi …

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1424107160_60070.doc energetik tð°sð°vvur. geyzenberg-shryodinger tð°sð°vvurlð°ri rejð: kirish tð°sð°vvurlð°r nð°zð°riyasi vð° kvð°ntlð°r nð°zð°riyasi ðsð¾siy qism: 1. kvð°nt tizimlð°rni turlichð° tð°sð°vvurlð°rdð° ifð¾dð°lð°sh 2.ðperð°tð¾rlð°rni turlichð° tð°sð°vvurlð°rdð° ifð¾dð°lð°sh xulð¾sð°: tð°sð°vvurlð°r nð°zð°riyasining fð°n vð° texnikð°dð°gi ð°hamiyati kvð°nt mexð°nikð°si keng fizik jð°rð°yonlð°rni oâz bð°grigð° ð¾lgð°nligi sð°bð°bidð°n tð°nlð°ngð°n bir usul mð°âlum guruh mð°sð°lð°lð°r uchun ð°nchð°yin qoâlð°y boâlsð°, bð¾shkð°si uchun nð¾qoâlð°y hisð¾blð°nishi mumkin. mð°sð°lð°n, shundð°y hð¾l boâlishi mumkinki, gilbert fð°zð¾sidð°gi ð°bstrð°kt vektð¾r hð¾lð°tlð°r (â«brð°â», â«ketâ» - dirð°k belgilð°shlð°ri) vð° dinð°mik kð°ttð°liklð°rgð° mð¾s keluvchi ð¾perð°tð¾rl...

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