For α = β, µ αβ (R) is referred to as the transition dipole between state |Φ α and |Φ β , while µ αα (R) is commonly referred to as the permanent dipole for state |Φ α . In a similar sense of defining the electronic Hamiltonian and corresponding eigenvalue equation for the matter, one can define the polaritonic Hamiltonian as Ĥpl ≡ ĤPF -TR , which includes all operators of molecules and cavity, except for the nuclear kinetic energy operator TR . As such, the polariton state is defined as the eigenstate of Ĥpl through the following eigenvalue problem