Eigensolution of Schrödinger Equation for Harmonically Bound Two-Body Coulomb System

Taking two identical ions in a Paul trap, we solved the SchrÖdinger equation for one-, two-, and three-dimensional harmonically bound two-body Coulomb models, in which the eigenfunctions are written in a series form and the eigenenergies are obtained from a continued fraction. Numerical calculations are made for specific discussion of two- and three-dimensional case. The comparison with a former one-dimensional approximate work shows that our result is more general and accurate.