İki ve üç boyutlu elektron gazının temel durum özelliklerinin analitik hesaplaması

The electron gas (2D and 3D) is a model which consists of interacting electrons moving in a uniform positive background. Its importance stems from the fact that a number of metals behave similarly, it provides the functional used in density functional theory, and that in 2D it can be experimentally realized. Understanding the behavior of this model is of fundamental importance. In this thesis we present an analysis of this model based on the Hypernetted Chain Method in 3D, and 2D. The HNC method is a variational method to calculate the ground state properties of an interacting system, by expressing the ground state energy as a functional of the radial distribution function. Minimizing the energy expression one obtains a zero energy Schrödinger equation for the square root of the radial distribution function. The potential in this equation can include the effects of fermionic or bosonic exchange. We applied this method to charged boson and electron gas in 2D and 3D systems. On the basis of the results of this research, it can be concluded that we obtained very close correlation energy results compared to Monte Carlo, and FHNC results for the density range when rs is from 0 to 20. This extended range is important for solid state applications.