由于周期性边界条件的使用，多体计算中出现了有限尺寸误差。作者的主要研究目的就是尽可能降低多体计算中的有限尺寸误差，为量子蒙特卡罗模拟的数据拟合提供帮助。本文从密度泛函理论出发，将有限尺寸效应引入GGA-PBE泛函，得到含尺寸效应的GGA-PBE泛函形式。讨论含尺寸效应的GGA-PBE泛函的极限情况，并与已知的含尺寸效应的LDA泛函进行对比，进而分析渐近行为。通过多体计算的数据得到修正后的GGA-PBE泛函的相关参数，展望其在多体计算中的应用。

On account of the use of periodic boundary conditions, finite size errors arise in many body calculations. The main purpose of the author’s research is to reduce the finite size errors in many body calculations as much as possible, which provides help for data fitting of Quantum Monte Carlo. Based on Density Functional Theory, The author takes finite size effect into consideration in GGA-PBE functional, and GGA-PBE functional form with finite size effect is obtained. The author compares GGA-PBE functional form with finite size effect with the known LDA functional with finite size effect. The parameters of GGA-PBE functional are obtained by the data of many body calculations, and its application in many body calculations is of bright prospect.