Abstract
The energy and wave function of a harmonically confined $N$-electron system coupled to light is calculated by separating the wave functions of the relative and center-of-mass (CM) motions. The light only couples to the CM variable, and the coupled equation can be solved analytically. The relative motion wave function has to be numerically approximated, but the relative Hamiltonian is independent of the coupling strength and it only gives a shift in the energy. The approach works for any coupling strength and the effective coupling strength can be increased by increasing the number of electrons. This gives an extra degree of freedom to fine tune the resonances and other properties of the light-matter coupled systems. Examples of wave functions of light-matter hybrid states are presented.
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