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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 Displacement operator ： ウィキペディア英語版 Displacement operator The displacement operator for one mode in quantum optics is the shift operator :$\backslash hat(\backslash alpha)=\backslash exp\; \backslash left\; (\; \backslash alpha\; \backslash hat^\backslash dagger\; -\; \backslash alpha^\backslash ast\; \backslash hat\; \backslash right\; )$, where $\backslash alpha$ is the amount of displacement in optical phase space, $\backslash alpha^$ * is the complex conjugate of that displacement, and $\backslash hat$ and $\backslash hat^\backslash dagger$ are the lowering and raising operators, respectively. The name of this operator is derived from its ability to displace a localized state in phase space by a magnitude $\backslash alpha$. It may also act on the vacuum state by displacing it into a coherent state. Specifically, $\backslash hat(\backslash alpha)|0\backslash rangle=|\backslash alpha\backslash rangle$ where $|\backslash alpha\backslash rangle$ is a coherent state, which is the eigenstates of the annihilation (lowering) operator. == Properties == The displacement operator is a unitary operator, and therefore obeys $\backslash hat(\backslash alpha)\backslash hat^\backslash dagger(\backslash alpha)=\backslash hat^\backslash dagger(\backslash alpha)\backslash hat(\backslash alpha)=\backslash hat$, where $\backslash hat$ is the identity operator. Since $\backslash hat^\backslash dagger(\backslash alpha)=\backslash hat(-\backslash alpha)$, the hermitian conjugate of the displacement operator can also be interpreted as a displacement of opposite magnitude ($-\backslash alpha$). The effect of applying this operator in a similarity transformation of the ladder operators results in their displacement. :$\backslash hat^\backslash dagger(\backslash alpha)\; \backslash hat\; \backslash hat(\backslash alpha)=\backslash hat+\backslash alpha$ :$\backslash hat(\backslash alpha)\; \backslash hat\; \backslash hat^\backslash dagger(\backslash alpha)=\backslash hat-\backslash alpha$ The product of two displacement operators is another displacement operator, apart from a phase factor, has the total displacement as the sum of the two individual displacements. This can be seen by utilizing the Baker-Campbell-Hausdorff formula. :$e^\; -\; \backslash alpha^$ *\hat} e^ - \beta^ *\hat} = e^ - (\beta^ *+\alpha^ *)\hat} e^. which shows us that: :$\backslash hat(\backslash alpha)\backslash hat(\backslash beta)=\; e^\; \backslash hat(\backslash alpha\; +\; \backslash beta)$ When acting on an eigenket, the phase factor $e^$ appears in each term of the resulting state, which makes it physically irrelevant.〔Christopher Gerry and Peter Knight: ''Introductory Quantum Optics''. Cambridge (England): Cambridge UP, 2005.〕 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「Displacement 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.