新exchange correlation energy的基態能量

Abstract

基態能量在量子力學上是代表最低的能量。在研究基態能量時，最主要的困難在於它其中的exchange correlation energy不是精確的表示式。有很多關於exchange correlation energy的估計。在此篇論文裡，我們表示的exchange correlation energy參考至[1]。而此篇文章的結果主要參考至[2]。我們先轉換原本能量的表示式，並且證明了基態能量的存在性。此外，我們也得到極小值的一些性質。

The ground state of a quantum mechanical system is its lowest-energy state. The main difficulty of the study of the ground state energy is that the exchange correlation energy is not the exact expression. There are many approximations about the exchange correlation energy. In this paper, the expression of the exchange correlation energy comes from [1]. First, we transform the form of the original total energy and prove the existence of the ground state energy. Besides, we also get some properties of the minimizer.