翻訳と辞書 Words near each other ・ Bogofilter ・ Bogogno ・ Bogogobo ・ Bogojci ・ Bogojevce ・ Bogojević ・ Bogojević Selo ・ Bogojevići ・ Bogojevo ・ Bogojina ・ Bogole, Nellore district ・ Bogolin ・ Bogoliubov causality condition ・ Bogoliubov inner product ・ Bogoliubov Prize (disambiguation) ・ Bogoliubov transformation ・ Bogoliubov–Parasyuk theorem ・ Bogoljub ・ Bogoljub Jevtić ・ Bogoljub Karić ・ Bogoljub Kočović ・ Bogoljub Kujundžić ・ Bogoljub Nedeljković ・ Bogoljub Šijaković ・ Bogolubovia ・ Bogolyubov ・ Bogolyubov Prize ・ Bogolyubov Prize (NASU) ・ Bogolyubov Prize for young scientists ・ Bogolyubovo 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 Bogoliubov transformation ： ウィキペディア英語版 Bogoliubov transformation In theoretical physics, the Bogoliubov transformation, named after Nikolay Bogolyubov, is a unitary transformation from a unitary representation of some canonical commutation relation algebra or canonical anticommutation relation algebra into another unitary representation, induced by an isomorphism of the commutation relation algebra. The Bogoliubov transformation is often used to diagonalize Hamiltonians, which yields the steady-state solutions of the corresponding Schrödinger equation. The solutions of BCS theory in a homogeneous system, for example, are found using a Bogoliubov transformation. The Bogoliubov transformation is also important for understanding the Unruh effect, Hawking radiation and many other topics. == Single bosonic mode example == Consider the canonical commutation relation for bosonic creation and annihilation operators in the harmonic basis :$\backslash left\; (\backslash hat,\; \backslash hat^\backslash dagger\; \backslash right)\; =\; 1~.$ Define a new pair of operators :$\backslash hat\; =\; u\; \backslash hat\; +\; v\; \backslash hat^\backslash dagger$ :$\backslash hat^\backslash dagger\; =\; u^$ * \hat^\dagger + v^ * \hat~, where the latter is the hermitian conjugate of the first. The Bogoliubov transformation is a canonical transformation of these operators. To find the conditions on the constants ''u'' and ''v'' such that the transformation is canonical, the commutator is evaluated, viz. :$\backslash left\; (\backslash hat,\; \backslash hat^\backslash dagger\; \backslash right)$ = \left (u \hat + v \hat^\dagger , u^ * \hat^\dagger + v^ * \hat \right ) = \cdots = \left ( |u|^2 - |v|^2 \right ) \left (\hat, \hat^\dagger \right ). It is then evident that $\backslash ,|u|^2\; -\; |v|^2\; =\; 1$ is the condition for which the transformation is canonical. Since the form of this condition is suggestive of the hyperbolic identity :$\backslash cosh^2\; x\; -\; \backslash sinh^2\; x\; =\; 1$, the constants and can be readily parametrized as :$u\; =\; e^\; \backslash cosh\; r$ :$v\; =\; e^\; \backslash sinh\; r\; ~\; .$ 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「Bogoliubov transformation」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.