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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 Electron-longitudinal acoustic phonon interaction ： ウィキペディア英語版 Electron-longitudinal acoustic phonon interaction Electron-longitudinal acoustic phonon interaction is an equation concerning atoms. ==Displacement operator of the longitudinal acoustic phonon== The equation of motions of the atoms of mass M which locates in the periodic lattice is : $M\; \backslash frac\; \}\; u\_\; =\; -k\_\; (\; u\_\; +\; u\_\; -2u\_\; )$, where $u\_$ is the displacement of the nth atom from their equilibrium positions. If we define the displacement $u\_$ of the nth atom by $u\_=\; x\_\; -\; la$, where $x\_$ is the coordinates of the lth atom and a is the lattice size, the displacement is given by $u\_=\; A\; e^$ Using Fourier transform, we can define : $Q\_\; =\; \backslash frac\; u\_\; e^$ and : $u\_\; =\; \backslash frac\; Q\_\; e^$. Since $u\_$ is a Hermite operator, : $u\_\; =\; \backslash frac\; (Q\_\; e^\; +\; Q^\_\; e^\; )$ From the definition of the creation and annihilation operator $a^\_\; =\; \backslash frac\; (M\backslash omega\_Q\_-iP\_),\; \backslash ;\; a\_\; =\; \backslash frac\; (M\backslash omega\_Q\_+iP\_)$ : $Q\_$ is written as : $Q\_\; =\; \backslash sqrt\; \}\}(a^\_+a\_)$ Then $u\_$ expressed as : $u\_\; =\; \backslash sum\_\; \backslash sqrt\; \}\}\; (a\_\; e^\; +\; a^\_\; e^)$ Hence, when we use continuum model, the displacement for the 3-dimensional case is : $u(r)\; =\; \backslash sum\_\; \backslash sqrt\; \}\; \}\; e\_\; (a\_\; e^\; +\; a^\_\; e^)$, where $e\_$ is the unit vector along the displacement direction. 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「Electron-longitudinal acoustic phonon interaction」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.