  The energy and wave function of a harmonically confined two-electron system
coupled to light is calculated by separating the wave functions of the relative
and center of mass (CM) motions. The relative motion wave function has a known
quasi-analytical solution. The light only couples to the CM variable and the
coupled equation can be solved with diagonalization without approximations. The
approach works for any coupling strength. Examples of wave functions of
light-matter hybrid states are presented.
