Matricya rozsiyannya abo S matricya operator yakij zv yazuye mizh soboyu pochatkovu i kincevu hvilovi funkciyi kvantovoyi sistemi pri rozsiyanni Poznachayetsya zazvichaj S displaystyle hat S ps S ps displaystyle psi infty hat S psi infty de ps displaystyle psi infty poznachaye hvilovu funkciyu v neskinchenno viddalenij moment chasu v minulomu do aktu rozsiyannya koli chastinki perebuvayut duzhe daleko odna vid odnoyi i vzayemodiyeyu mizh nimi mozhna znehtuvati a ps displaystyle psi infty poznachaye hvilovu funkciyu v neskinchenno viddalenij moment chasu pislya aktu rozsiyannya koli znovu zh chastinki vzhe vstigli rozletitisya na taku viddal sho vzayemodiyeyu mizh nimi mozhna znehtuvati S matricya unitarna tobto S S 1 displaystyle hat S dagger hat S 1 de znachok displaystyle dagger poznachaye ermitove spryazhennya Zmist 1 Operator perehodu 2 Rozklad 3 Imovirnist perehodu 3 1 Imovirnist perehodu v odinicyu chasu 4 Istoriya 5 Div takozh 6 DzherelaOperator perehodu red Operator T S 1 displaystyle hat mathcal T hat S 1 nbsp nazivayut operatorom perehodu Rozklad red Gamiltonian sistemi chastinok yaki rozsiyuyutsya odna na inshij mozhna zapisati u viglyadi H H 0 V H 0 V displaystyle hat H hat H 0 hat V hat H 0 prime hat V prime nbsp V comu virazi gamiltonian sistemi chastinok do rozsiyannya i pislya nogo rozbivayetsya na rizni skladovi dlya zagalnosti pri zitknennyah sklad sistemi mozhe zminitisya napriklad elektron mozhe vibiti inshij elektron iz atoma Yaksho funkciyi f a displaystyle varphi alpha nbsp ye vlasnimi funkciyami operatora H 0 displaystyle hat H 0 nbsp H 0 f a E a f a displaystyle hat H 0 varphi alpha E alpha varphi alpha nbsp a funkciyi f b displaystyle varphi beta nbsp ye vlasnimi funkciyami operatora H 0 displaystyle hat H 0 prime nbsp H 0 f b E b f b displaystyle hat H 0 prime varphi beta E beta varphi beta nbsp to hvilovu funkciyu pochatkovogo i kincevogo staniv mozhna rozklasti ps a c a f a displaystyle psi infty sum alpha c alpha varphi alpha nbsp ps b c b f b displaystyle psi infty sum beta tilde c beta varphi beta nbsp Todi c b a S b a c a displaystyle tilde c beta sum alpha S beta alpha c alpha nbsp Iz cogo virazu vidno sho S b a displaystyle S beta alpha nbsp ye matriceyu zagalom neskinchennogo rangu Zavdyaki comu S matricya j otrimala svoyu nazvu Imovirnist perehodu red Imovirnist perehodu sistemi iz stanu a displaystyle alpha nbsp v stan b displaystyle beta nbsp viznachayetsya elementom matrici perehodu T b a displaystyle mathcal T beta alpha nbsp W a b T b a 2 displaystyle W alpha rightarrow beta mathcal T beta alpha 2 nbsp Imovirnist perehodu v odinicyu chasu red Beruchi do uvagi sho energiya sistemi ye integralom ruhu matricya perehodu zapisuyetsya u viglyadi T b a 2 p i t b a d E a E b displaystyle mathcal T beta alpha 2 pi it beta alpha delta E alpha E beta nbsp Todi zagalna imovirnist perehodu za neskinchennij promizhok chasu W a b displaystyle W alpha rightarrow beta nbsp dorivnyuye W a b 2 p 2 t b a 2 d E a E b 2 2 p 2 t b a 2 d E a E b lim T 1 2 p ℏ 1 2 T 1 2 T d t exp i ℏ E a E b t 2 p ℏ t b a 2 d E a E b lim T T displaystyle W alpha rightarrow beta 2 pi 2 t beta alpha 2 delta E alpha E beta 2 2 pi 2 t beta alpha 2 delta E alpha E beta lim T to infty frac 1 2 pi hbar int frac 1 2 T frac 1 2 T dt exp left frac i hbar E alpha E beta t right frac 2 pi hbar t beta alpha 2 delta E alpha E beta lim T to infty T nbsp Imovirnist perehodu v odinicyu chasu w a b displaystyle w alpha rightarrow beta nbsp oderzhimo podilivshi povnu imovirnist W a b displaystyle W alpha rightarrow beta nbsp na povnij promizhok chasu T displaystyle T nbsp w a b 2 p ℏ t b a 2 d E a E b displaystyle w alpha rightarrow beta frac 2 pi hbar t beta alpha 2 delta E alpha E beta nbsp Istoriya red Matricyu rozsiyannya vviv u obig v 1937 roci Dzhon Viler a v 1940 roci cyu ideyu pidhopiv Verner Gejzenberg Div takozh red Operator evolyuciyiDzherela red Sitenko O G Teoriya rozsiyannya K Libid 1993 332 s nbsp Ce nezavershena stattya z fiziki Vi mozhete dopomogti proyektu vipravivshi abo dopisavshi yiyi Otrimano z https uk wikipedia org w index php title Matricya rozsiyannya amp oldid 27506813
