Two electrons in harmonic confinement coupled to light in a cavity

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.