Taking two identical ions in a Paul trap, we solved the Schrodinger eq
uation for one-, two-, and three-dimensional harmonically bound two-bo
dy Coulomb models, in which the eigenfunctions are written in a series
form and the eigenenergies are obtained from a continued fraction. Nu
merical calculations are made for specific discussion of two- and thre
e-dimensional case. The comparison with a former one-dimensional appro
ximate work shows that our result is more general and accurate.