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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 Plane wave expansion ： ウィキペディア英語版 Plane wave expansion In physics, the plane wave expansion expresses a plane wave as a sum of spherical waves, : $e^\; =\; \backslash sum\_^\backslash infty\; (2\; \backslash ell\; +\; 1)\; i^\backslash ell\; j\_\backslash ell(k\; r)\; P\_\backslash ell(\backslash hat\; \backslash cdot\; \backslash hat)$, where * is the imaginary unit, * is a wave vector of length , * is a position vector of length , * are spherical Bessel functions, * are Legendre polynomials, and * the hat denotes the unit vector. In the special case where is aligned with the z-axis, : $e^\; =\; \backslash sum\_^\backslash infty\; (2\; \backslash ell\; +\; 1)\; i^\backslash ell\; j\_\backslash ell(k\; r)\; P\_\backslash ell(\backslash cos\; \backslash theta)$, where is the spherical polar angle of . == Expansion in spherical harmonics == With the spherical harmonic addition theorem the equation can be rewritten as : $e^\}\; =\; 4\; \backslash pi\; \backslash sum\_^\backslash infty\; \backslash sum\_^\backslash ell\; i^\backslash ell\; j\_\backslash ell(k\; r)\; Y\_\backslash ell^m)$, where * are the spherical harmonics and * the superscript denotes complex conjugation. Note that the complex conjugation can be interchanged between the two spherical harmonics due to symmetry. 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「Plane wave expansion」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.