The energy spectra of two interacting electrons confined in a quantum dot of two and three dimensions are calculated by using the shifted 1/D expansion method. We have shown the dependence of the electron-electron interaction energy on the dimensionality of the quantum dot. An explanation is given for the energy level crossings and transitions in the angular momentum of the ground state of the quantum dot. Based on comparision, the shifted 1/D expansion method is an accurate and effective tool to produce and explain the spectral properties of the quantum dot.