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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 Coulomb wave function ： ウィキペディア英語版 Coulomb wave function In mathematics, a Coulomb wave function is a solution of the Coulomb wave equation, named after Charles-Augustin de Coulomb. They are used to describe the behavior of charged particles in a Coulomb potential and can be written in terms of confluent hypergeometric functions or Whittaker functions of imaginary argument. ==Coulomb wave equation== The Coulomb wave equation for a single charged particle is the Schrödinger equation with Coulomb potential :$\backslash left(-\backslash frac+\backslash frac\backslash right)\; \backslash psi\_)\; =\; \backslash frac\; \backslash psi\_)\; \backslash ,,$ where $Z=Z\_1\; Z\_2$ is the product of the charges of the particle and of the field source (in units of the elementary charge, $Z=-1$ for hydrogen atom) and $k^2$ is proportional to the asymptotic energy of the particle. The solution – Coulomb wave function – can be found by solving this equation in parabolic coordinates :$\backslash xi=\; r\; +\; \backslash vec\backslash cdot\backslash hat,\; \backslash quad\; \backslash zeta=\; r\; -\; \backslash vec\backslash cdot\backslash hat\; \backslash qquad\; (\backslash hat\; =\; \backslash vec/k)\; \backslash ,.$ Depending on the boundary conditions chosen the solution has different forms. Two of the solutions are :$\backslash psi\_(\backslash vec)\; =\; \backslash frac\; e^\}\; M(\backslash mp\; i\backslash eta,\; 1,\; \backslash pm\; ikr\; -\; i\backslash vec\backslash cdot\backslash vec)\; \backslash ,,$ where $M(a,b,z)\; \backslash equiv\; (\backslash vec)\; \backslash rightarrow\; \backslash frac\backslash cdot\backslash vec\}\; \backslash qquad\; (\backslash vec\backslash cdot\backslash vec\; \backslash rightarrow\; \backslash mp\backslash infty)\; \backslash ,,$ which correspond to $\backslash vec$-oriented plane-wave asymptotic state ''before'' or ''after'' its approach of the field source at the origin, respectively. The functions $\backslash psi\_$ are related to each other by the formula :$\backslash psi\_\; =\; \backslash psi\_\; \backslash ,.$ 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「Coulomb wave function」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.