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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 Two-electron atom ： ウィキペディア英語版 Two-electron atom In atomic physics, a two-electron atom or helium-like ion is a quantum mechanical system consisting of one nucleus with a charge of ''Ze'' and just two electrons. This is the first case of many-electron systems where the Pauli exclusion principle plays a central role. It is an example of a three-body problem. The first few two-electron atoms are: ==Schrödinger equation== The Schrödinger equation for any two-electron system, such as the neutral Helium atom (He, ''Z'' = 2), the negative Hydrogen ion (H−, ''Z'' = 1), or the positive Lithium ion (Li+, ''Z'' = 3) is:〔Physics of Atoms and Molecules, B.H. Bransden, C.J.Joachain, Longman, 1983, ISBN 0-582-44401-2〕 For a more rigorous mathematical derivation of Schrödinger's equation, see also.〔 :$E\backslash psi\; =\; -\backslash hbar^2\backslash left(+\backslash nabla\_2^2\; \backslash right)\; +\; \backslash frac\backslash nabla\_1\backslash cdot\backslash nabla\_2\backslash right)\; \backslash psi\; +\; \backslash frac\backslash left(\backslash frac+\backslash frac\; \backslash right)\; \backslash right)\; \backslash psi$ where r1 is the position of one electron (''r''1 = |r1| is its magnitude), r2 is the position of the other electron (''r''2 = |r2| is the magnitude), ''r''12 = |r12| is the magnitude of the separation between them given by :$|\backslash bold\_|\; =\; |\backslash bold\_2\; -\; \backslash bold\_1\; |\; \backslash ,\backslash !$ ''μ'' is again the two-body reduced mass of an electron with respect to the nucleus of mass ''M'', so this time :$\backslash mu\; =\; \backslash frac\; \backslash ,\backslash !$ and ''Z'' is the atomic number for the element (not a quantum number). The cross-term of two laplacians :$\backslash frac\backslash nabla\_1\backslash cdot\backslash nabla\_2\backslash ,\backslash !$ is known as the ''mass polarization term'', which arises due to the motion of atomic nuclei. The wavefunction is a function of the two electron's positions: :$\backslash psi\; =\; \backslash psi(\backslash bold\_1,\backslash bold\_2)$ There is no closed form solution for this equation. 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「Two-electron atom」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.