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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 Jellium ： ウィキペディア英語版 Jellium Jellium, also known as the uniform electron gas (UEG) or homogeneous electron gas (HEG), is a quantum mechanical model of interacting electrons in a solid where the positive charges (i.e. atomic nuclei) are assumed to be uniformly distributed in space whence the electron density is a uniform quantity as well in space. This model allows one to focus on the effects in solids that occur due to the quantum nature of electrons and their mutual repulsive interactions (due to like charge) without explicit introduction of the atomic lattice and structure making up a real material. Jellium is often used in solid-state physics as a simple model of delocalized electrons in a metal, where it can qualitatively reproduce features of real metals such as screening, plasmons, Wigner crystallization and Friedel oscillations. At zero temperature, the properties of jellium depend solely upon the constant electronic density. This lends it to a treatment within density functional theory; the formalism itself provides the basis for the local-density approximation to the exchange-correlation energy density functional. The term ''jellium'' was coined by Conyers Herring, alluding to the "positive jelly" background, and the typical metallic behavior it displays. ==Hamiltonian== The jellium model treats the electron-electron coupling rigorously. The artificial and structureless background charge interacts electrostatically with itself and the electrons. The jellium Hamiltonian for ''N''-electrons confined within a volume of space Ω, and with electronic density ''ρ''(r) and background charge density ''n''(R) = ''N''/Ω is :$\backslash hat=\backslash hat\_\_\_\_^N\backslash frac+\backslash sum\_^N\backslash frac\_j|\}$ *''H''back is the Hamiltonian of the positive background charge interacting electrostatically with itself: ::$\backslash hat\_\backslash int\_\backslash mathrm\backslash mathbf\backslash int\_\backslash mathrm\backslash mathbf\text{'}\backslash \; \backslash frac\text{'})\}\text{'}|\}\; =\; \backslash frac\backslash left(\backslash frac\backslash right)^\backslash int\_\backslash mathrm\backslash mathbf\backslash int\_\backslash mathrm\backslash mathbf\text{'}\backslash \; \backslash frac\text{'}|\}$ *''H''el-back is the electron-background interaction Hamiltonian, again an electrostatic interaction: ::$\backslash hat\_\backslash mathrm\backslash mathbf\backslash int\_\backslash mathrm\backslash mathbf\backslash \; \backslash frac)\}|\}\; =\; -e^\backslash frac\backslash sum\_^\backslash int\_\backslash mathrm\backslash mathbf\backslash \; \backslash frac-\backslash mathbf|\}$ ''H''back is a constant and, in the limit of an infinite volume, divergent along with ''H''el-back. The divergence is canceled by a term from the electron-electron coupling: the background interactions cancel and the system is dominated by the kinetic energy and coupling of the electrons. Such analysis is done in Fourier space; the interaction terms of the Hamiltonian which remain correspond to the Fourier expansion of the electron coupling for which q ≠ 0. 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「Jellium」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.