Approximate Series Solutions of Nonseparable Schrödinger Equations. II. General Three-Particle System with Coulomb Interaction

The series solution method developed by Pekeris for the Schrödinger wave equation of two-electron atoms has been generalized to handle any three particles with Coulomb interaction. Calculations have been carried out with wavefunctions through the sixth degree which result in a linear combination of 84 terms for the unsymmetrical case. Systems for which numerical results are given are: the hydride ion with nuclear motion, the trielectron (e+e—e—) or positronium ion, the positron—hydrogen atom interaction (e+e—p+), and the mu-mesonic isotopic hydrogen molecule-ion (p+μ—d+).