Words near each other
 ・ Displacement ・ Displacement (fencing) ・ Displacement (fluid) ・ Displacement (linguistics) ・ Displacement (orthopedic surgery) ・ Displacement (psychology) ・ Displacement (ship) ・ Displacement (vector) ・ Displacement activity ・ Displacement chess ・ Displacement chromatography ・ Displacement current ・ Displacement field ・ Displacement field (mechanics) ・ Displacement mapping ・ Displacement operator ・ Displacement receiver ・ Displacement ventilation ・ Displacement Volumetric Meter ・ Displacement–length ratio ・ Displacer (band) ・ Displacer (disambiguation) ・ Displacer beast ・ Displacer serpent ・ Displair ・ Display ・ Display (horse) ・ Display (zoology) ・ Display advertising ・ Display aspect ratio
 Dictionary Lists
 mini英和辞書
 mini和英辞書
 Webster 1913
 Latin-English
 FOLDOC
 Wikipedia English
 ウィキペディア
 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
:$\hat\left(\alpha\right)=\exp \left \left( \alpha \hat^\dagger - \alpha^\ast \hat \right \right)$,
where $\alpha$ is the amount of displacement in optical phase space, $\alpha^$
* is the complex conjugate of that displacement, and $\hat$ and $\hat^\dagger$ 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 $\alpha$. It may also act on the vacuum state by displacing it into a coherent state. Specifically,
$\hat\left(\alpha\right)|0\rangle=|\alpha\rangle$ where $|\alpha\rangle$ is a coherent state, which is the eigenstates of the annihilation (lowering) operator.
== Properties ==
The displacement operator is a unitary operator, and therefore obeys
$\hat\left(\alpha\right)\hat^\dagger\left(\alpha\right)=\hat^\dagger\left(\alpha\right)\hat\left(\alpha\right)=\hat$,
where $\hat$ is the identity operator. Since $\hat^\dagger\left(\alpha\right)=\hat\left(-\alpha\right)$, the hermitian conjugate of the displacement operator can also be interpreted as a displacement of opposite magnitude ($-\alpha$). The effect of applying this operator in a similarity transformation of the ladder operators results in their displacement.
:$\hat^\dagger\left(\alpha\right) \hat \hat\left(\alpha\right)=\hat+\alpha$
:$\hat\left(\alpha\right) \hat \hat^\dagger\left(\alpha\right)=\hat-\alpha$
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.
:$e^ - \alpha^$
*\hat} e^ - \beta^
*\hat} = e^ - (\beta^
*+\alpha^
*)\hat} e^.
which shows us that:
:$\hat\left(\alpha\right)\hat\left(\beta\right)= e^ \hat\left(\alpha + \beta\right)$
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.〕

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