WikiDer > Zarrachalar soni operatori

Yilda kvant mexanikasi, jami bo'lgan tizimlar uchun zarrachalar soni saqlanib qolmasligi mumkin raqam operatori bo'ladi kuzatiladigan bu zarralar sonini hisoblaydi.

Raqam operatori ishlaydi Bo'sh joy. Ruxsat bering

${displaystyle | Psi burchagi _ {u} = | phi _ {1}, phi _ {2}, cdots, phi _ {n} burchak _ {u}}$

bo'lishi a Fok holati, bitta zarrachali holatlardan tashkil topgan ${displaystyle | phi _ {i} burchak}$ dan chizilgan asos Fok fazosining asosiy Hilbert makonining. Tegishli narsa berilgan yaratish va yo'q qilish operatorlari ${displaystyle a ^ {xanjar} (phi _ {i})}$ va ${displaystyle a (phi _ {i}),}$ raqam operatorini aniqlaymiz

${displaystyle {hat {N_ {i}}} {stackrel {mathrm {def}} {=}} a ^ {xanjar} (phi _ {i}) a (phi _ {i})}$

va bizda bor

${displaystyle {hat {N_ {i}}} | Psi burchagi _ {u} = N_ {i} | Psi burchagi _ {u}}$

qayerda ${displaystyle N_ {i}}$ holatdagi zarrachalar soni ${displaystyle | phi _ {i} burchak}$. Yuqoridagi tenglikni ta'kidlash bilan isbotlash mumkin

${displaystyle {egin {matrix} a (phi _ {i}) | phi _ {1}, phi _ {2}, cdots, phi _ {i-1}, phi _ {i}, phi _ {i + 1 }, cdots, phi _ {n} angle _ {u} & = & {sqrt {N_ {i}}} | phi _ {1}, phi _ {2}, cdots, phi _ {i-1}, phi _ {i + 1}, cdots, phi _ {n} burchak _ {u} a ^ {xanjar} (phi _ {i}) | phi _ {1}, phi _ {2}, cdots, phi _ { i-1}, phi _ {i + 1}, cdots, phi _ {n} angle _ {u} & = & {sqrt {N_ {i}}} | phi _ {1}, phi _ {2}, cdots, phi _ {i-1}, phi _ {i}, phi _ {i + 1}, cdots, phi _ {n} angle _ {u} end {matrix}}}$

keyin

${displaystyle {egin {matrix} {hat {N_ {i}}} | Psi burchagi _ {u} = a ^ {xanjar} (phi _ {i}) a (phi _ {i}) | phi _ {1} , phi _ {2}, cdots, phi _ {i-1}, phi _ {i}, phi _ {i + 1}, cdots, phi _ {n} burchak _ {u} & = & {sqrt {N_ {i}}} a ^ {xanjar} (phi _ {i}) | phi _ {1}, phi _ {2}, cdots, phi _ {i-1}, phi _ {i + 1}, cdots, phi _ {n} angle _ {u} & = & {sqrt {N_ {i}}} {sqrt {N_ {i}}} | phi _ {1}, phi _ {2}, cdots, phi _ { i-1}, phi _ {i}, phi _ {i + 1}, cdots, phi _ {n} angle _ {u} & = & N_ {i} | Psi burchagi _ {u} end {matrix} }}$

Shuningdek qarang

• Harmonik osilator
• Kvantli harmonik osilator
• Ikkinchi kvantlash
• Kvant maydoni nazariyasi
• Termodinamika
• Fermion raqamlari operatori

Adabiyotlar

• Brus, Xenrik; Flensberg, Karsten. (2004). Kondensatlangan fizikada ko'p tanali kvant nazariyasi: kirish. Oksford universiteti matbuoti. ISBN 0-19-856633-6.CS1 maint: bir nechta ism: mualliflar ro'yxati (havola)
• Fradkin tomonidan ikkinchi kvantizatsiya yozuvlari