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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 Born approximation ： ウィキペディア英語版 Born approximation In scattering theory and, in particular in quantum mechanics, the Born approximation consists of taking the incident field in place of the total field as the driving field at each point in the scatterer. The Born approximation is named after Max Born who proposed this approximation in early days of quantum theory development. It is the perturbation method applied to scattering by an extended body. It is accurate if the scattered field is small, compared to the incident field, in the scatterer. For example, the radar scattering of radio waves by a light styrofoam column can be approximated by assuming that each part of the plastic is polarized by the same electric field that would be present at that point without the column, and then calculating the scattering as a radiation integral over that polarization distribution. ==Born approximation to the Lippmann–Schwinger equation== The Lippmann–Schwinger equation for the scattering state $\backslash vert\}\backslash rangle$ with a momentum p and out-going (+) or in-going (−) boundary conditions is :$\backslash vert\}\backslash rangle\; =\; \backslash vert\}\backslash rangle\; +\; G^\backslash circ(E\_p\; \backslash pm\; i\backslash epsilon)\; V\; \backslash vert\}\backslash rangle$ where $G^\backslash circ$ is the free particle Green's function, $\backslash epsilon$ is a positive infinitesimal quantity, and ''V'' the interaction potential. $\backslash vert\}\backslash rangle$ is the corresponding free scattering solution sometimes called incident field. The factor $\backslash vert\}\backslash rangle$ on the right hand side is sometimes called ''driving field''. This equation becomes within Born approximation :$\backslash vert\}\backslash rangle\; =\; \backslash vert\}\backslash rangle\; +\; G^\backslash circ(E\_p\; \backslash pm\; i\backslash epsilon)\; V\; \backslash vert\}\backslash rangle$ which is much easier to solve since the right hand side does not depend on the unknown state $\backslash vert\}\backslash rangle$ anymore. The obtained solution is the starting point of the Born series. 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「Born approximation」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.