Finding the Ground State Energy for the Helium Atom in a 2D Configuration by Using the Solutions of a Four-spinor Dirac-like Equation

Abstract

We give a two-dimensional analysis of the classical conservation theorem-derived two-electron problem, from which we derive a particular form of the Dirac equation for the helium atom. Although in theory this problem can be solved analytically, approximate solutions for it are given using two different approaches. One approach is a Hylleraas-type variational approach, the execution of which is postponed until a subsequent communication. The set of equations in the alternative method will be divided into its angular and radial components for a more thorough study. Additionally, just for the fundamental state of the atom, an accurate solution for the angular component and an approximative solution for the radial component will be shown.