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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 Kramers-Heisenberg formula ： ウィキペディア英語版 Kramers–Heisenberg formula The Kramers-Heisenberg dispersion formula is an expression for the cross section for scattering of a photon by an atomic electron. It was derived before the advent of quantum mechanics by Hendrik Kramers and Werner Heisenberg in 1925, based on the correspondence principle applied to the classical dispersion formula for light. The quantum mechanical derivation was given by Paul Dirac in 1927. The Kramers–Heisenberg formula was an important achievement when it was published, explaining the notion of "negative absorption" (stimulated emission), the Thomas-Reiche-Kuhn sum rule, and inelastic scattering - where the energy of the scattered photon may be larger or smaller than that of the incident photon - thereby anticipating the Raman effect. == Equation == The Kramers-Heisenberg (KH) formula for second order processes is 〔〔J.J. Sakurai, Advanced Quantum Mechanics, Addison-Wesley (1967), page 56.〕 $\backslash frac=\backslash frac\backslash sum\_\backslash left\; |\; \backslash sum\_\; \backslash frac\}\backslash right\; |^2\; \backslash delta\; (E\_i\; -\; E\_f\; +\; \backslash hbar\; \backslash omega\_k\; -\; \backslash hbar\; \backslash omega\_k^\backslash prime)$ It represents the probability of the emission of photons of energy $\backslash hbar\; \backslash omega\_k^\backslash prime$ in the solid angle $d\backslash Omega\_$ (centred in the $k^\backslash prime$ direction), after the excitation of the system with photons of energy $\backslash hbar\; \backslash omega\_k$. $|i\backslash rangle,\; |n\backslash rangle,\; |f\backslash rangle$ are the initial, intermediate and final states of the system with energy $E\_i\; ,\; E\_n\; ,\; E\_f$ respectively; the delta function ensures the energy conservation during the whole process. $T$ is the relevant transition operator. $\backslash Gamma\_n$ is the instrinsic linewidth of the intermediate state. 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「Kramers–Heisenberg formula」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.