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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 Hartree equation ： ウィキペディア英語版 Hartree equation In 1927, a year after the publication of the Schrödinger equation, Hartree formulated what are now known as the Hartree equations for atoms, using the concept of ''self-consistency'' that Lindsay had introduced in his study of many electron systems in the context of Bohr theory. Hartree assumed that the nucleus together with the electrons formed a spherically symmetric field. The charge distribution of each electron was the solution of the Schrödinger equation for an electron in a potential $v(r)$, derived from the field. Self-consistency required that the final field, computed from the solutions was self-consistent with the initial field and he called his method the self-consistent field method. In order to solve the equation of an electron in a spherical potential, Hartree first introduced atomic units to eliminate physical constants. Then he converted the Laplacian from Cartesian to spherical coordinates to show that the solution was a product of a radial function $P(r)/r$ and a spherical harmonic with an angular quantum number $\backslash ell$, namely $\backslash psi=(1/r)P(r)S\_\backslash ell(\backslash theta,\backslash phi)$. The equation for the radial function was :$d^2P(r)/dr^2\; +\; (-\; \backslash ell(\backslash ell+1)/r^2)P(r)=0.$ In mathematics, the Hartree equation, named after Douglas Hartree, is :$i\backslash ,\backslash partial\_tu\; +\; \backslash nabla^2\; u=\; V(u)u$ in $\backslash mathbb^$ where :$V(u)=\; \backslash pm\; |x|^$ * |u|^2 and : The non-linear Schrödinger equation is in some sense a limiting case. ==External links== * 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「Hartree equation」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.