Direct Numerical Solution of the Three-Body Problem

Abstract

We discuss a numerical method to determine the binding energy and the wave function for a three-body system. Radial wave functions of the form ${g}_{1}({r}_{1}){g}_{2}({r}_{2}){g}_{3}({r}_{3})$ are used, ${r}_{1}$, ${r}_{2}$, and ${r}_{3}$ being the interparticle distances. The method is applied to ${\mathrm{He}}^{3}$ and ${\mathrm{H}}^{3}$ with central forces and hard core to show the accuracy and the speed of the calculation.