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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク particle number operator ： ウィキペディア英語版 particle number operator In quantum mechanics, for systems where the total number of particles may not be preserved, the number operator is the observable that counts the number of particles. The number operator acts on Fock space. Let :$|\backslash Psi\backslash rangle\_\backslash nu=|\backslash phi\_1,\backslash phi\_2,\backslash cdots,\backslash phi\_n\backslash rangle\_\backslash nu$ be a Fock state, composed of single-particle states $|\backslash phi\_i\backslash rangle$ drawn from a basis of the underlying Hilbert space of the Fock space. Given the corresponding creation and annihilation operators $a^(\backslash phi\_i)$ and $a(\backslash phi\_i)\backslash ,$ we define the number operator by :$\backslash hat\; \backslash \; \backslash stackrel\backslash \; a^(\backslash phi\_i)a(\backslash phi\_i)$ and we have :$\backslash hat|\backslash Psi\backslash rangle\_\backslash nu=N\_i|\backslash Psi\backslash rangle\_\backslash nu$ where $N\_i$ is the number of particles in state $|\backslash phi\_i\backslash rangle$. The above equality can be proven by noting that :$\backslash begin$ a(\phi_i) |\phi_1,\phi_2,\cdots,\phi_,\phi_i,\phi_,\cdots,\phi_n\rangle_\nu &=& \sqrt |\phi_1,\phi_2,\cdots,\phi_,\phi_,\cdots,\phi_n\rangle_\nu \\ a^(\phi_i) |\phi_1,\phi_2,\cdots,\phi_,\phi_,\cdots,\phi_n\rangle_\nu &=& \sqrt |\phi_1,\phi_2,\cdots,\phi_,\phi_,\phi_,\cdots,\phi_n\rangle_\nu \end then :$\backslash begin$ \hat|\Psi\rangle_\nu = a^(\phi_i)a(\phi_i) |\phi_1,\phi_2,\cdots,\phi_,\phi_i,\phi_,\cdots,\phi_n\rangle_\nu &=& \sqrt a^(\phi_i) |\phi_1,\phi_2,\cdots,\phi_,\phi_,\cdots,\phi_n\rangle_\nu \\ &=& \sqrt \sqrt |\phi_1,\phi_2,\cdots,\phi_,\phi_,\phi_,\cdots,\phi_n\rangle_\nu \\&=& N_i|\Psi\rangle_\nu\\ \end ==See also== *Harmonic oscillator *Quantum harmonic oscillator *Second quantization *Quantum field theory *Thermodynamics *Fermion number operator 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「particle number operator」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.