The series solution method in quantum chemistry for three-particle systems

In this contribution we discuss how the series solution method can be used effectively to probe the bound state stability of three-particle systems. We demonstrate the versatility of the method by presenting results of a variational method for calculating the threshold values of particle mass or particle charge for the formation of a bound state. By treating all the particles on an equal footing, we explore the effects of nuclear motion in diatomic ions and electron correlation in two-electron atomic systems.