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In quantum chemistry and physics, the Lieb–Oxford inequality provides a lower bound for the indirect part of the Coulomb energy of a quantum mechanical system. It is named after Elliott H. Lieb and Stephen Oxford. The inequality is of importance for density functional theory and plays a role in the proof of stability of matter. ==Introduction== In classical physics, one can calculate the Coulomb energy of a configuration of charged particles in the following way. First, calculate the charge density , where is a function of the coordinates . Second, calculate the Coulomb energy by integrating: : In other words, for each pair of points and , this expression calculates the energy related to the fact that the charge at is attracted to or repelled from the charge at . The factor of corrects for double-counting the pairs of points. In quantum mechanics, it is ''also'' possible to calculate a charge density , which is a function of . More specifically, is defined as the expectation value of charge density at each point. But in this case, the above formula for Coulomb energy is not correct, due to exchange and correlation effects. The above, classical formula for Coulomb energy is then called the "direct" part of Coulomb energy. To get the ''actual'' Coulomb energy, it is necessary to add a correction term, called the "indirect" part of Coulomb energy. The Lieb–Oxford inequality concerns this indirect part. It is relevant in density functional theory, where the expectation value ρ plays a central role. 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「Lieb–Oxford inequality」の詳細全文を読む スポンサード リンク
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