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 $g_1\left(r_1\right)g_2\left(r_2\right)g_3\left(r_3\right)$ 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.