Operatorho

Operatorho dar nazariyai k v a n t i, mafhumi matematikiest, ki dar apparata matematikii mekha­nikai kvanti va nazariyai kvantii maydon istifoda meshavad va baroi ba vektori muayyani holat yo (funk­siyai mavji) V muvofiq guzoshtani digar vektorhoi (funksiyahoi) muayyan khizmat mekunad. Vobastagii bayni Ch^g va ‘R’ dar shakli

A

‘G’ = L‘Y ifoda meshavad, ki dar on A

L operator ast. Dar mekhanikai kvan­ti ba har yak buzurgihoi fiziki (koordinata, impuls, momenti miqdori harakat, energiya va gayra) operatori L (operatori koordinataho, operatori imnuls va gayra) muvofiq guzoshta meshavad, ki ba vektori holat yo funksiyai mavji (buzurgie, ki holati sistemam fizikiro tavsif medihad) tasir merasonad.

Operatorhoi odditarini ba funk­siyai mavjii ChG(kh) (kh — koordina­tai zarra) tasirkunanda operatori zarb (masalan, operatori koordinatai

A A

kh, khCh^,= khCh’| va operatori differensironi (masalan, operatori impuls R, a         . dchg

RCh? = —i        , i — vodidi mavhum,

1C — sobitai Plank) meboshand. Agar W vektore boshad, ki komponentahoyashro dar shakli sutuni adadho ifo­da kardan mumkin ast, on goh ope­rator az jadvali kvadrati — matri­sa iborat meshavad.

Dar mekhanikai kvanti asosan ope­ratorhoi khatti istifoda meshavand. Zero onho ba khosiyathoi zerin sohiband: agar LV» = va Wt = Fa’

A

boshad, L(c,’P, + s₂ChG₂) =»e,ChG/ + caW (S| va s₂ — adadhoi kompleksi) ast. In khosiyat yake az prisiphoi asosii mekhanikai kvanti — prinsipi  superpozisiyaro inikos me­kunad.