Observables of the three body Coulomb Problem

Abstract

The Coulomb three body problem is solved using a variational approach. We consider only S-wave solutions in this work. The wave function is expanded in products of Laguerre polynomials which are coordinate functions of perimetric coordinates. These choices follow from the work of Liverts and Barnea, whose Mathematica code was used for the calculation of energy and wave function coefficients. Observables of Helium are calculated for a single and seven state wave function expansion. Additionally, for the single state problem, the energy correction due to the finite size of alpha particle is calculated and determined to be negligible. There is agreement between the results of this work and that of similar literature. Future work includes a resolution study of the expectation values as a function of the wave function expansion size.