We are going to study two electrons in a harmonic oscillator well which also interact via a repulsive Coulomb interaction. Let us start with the single-electron equation written as −ℏ22md2dr2u(r)+12kr2u(r)=E(1)u(r), where E(1) stands for the energy with one electron only. For two electrons with no repulsive Coulomb interaction, we have the following Schroedinger equation (−ℏ22md2dr21−ℏ22md2dr22+12kr21+12kr22)u(r1,r2)=E(2)u(r1,r2).