where the only photonic operator that appears is that of the photonic Hamiltonian Ĥph = ħω c â † â + 1 2 whose eigenstates are the vacuum Fock states | ñ ⟩ in the rotated GCS basis (which have the same frequency but with a shift in position q c by Z compared to the vacuum Fock states). One should note that the Pauli-Fierz Fock states can be reobtained by applying the reverse unitary coherent state transformation ÛGCS (Eq. 27) to the resulting Fock states after the self-consistent solution (discussed below) of Eq. 30 has been achieved, whose average photon number will depend on the self-consistent solution of the dipole moment ⟨ μ⟩ HF = 0. suggesting that molecules with strong ground-state dipole moments will exhibit stronger polaritonic effects. The ground polaritonic state can be defined as the |HF, 0⟩ wavefunction. Neglecting the photonic zero-point