As n decreases, the potential becomes increasingly non-local. These numerical results are for an electron in a double well potential (similar to panel (b)). it only strongly couples the |E α ⟩ and |E β ⟩ energy levels when their energies are close. The transition dipole operator for a single electron is μ = -x (where the fundamental charge of the electron is z = -1), and thus µ αβ = -x αβ . This explains why Ĥd•E often gives accurate numerical results of polariton eigenvalues, due to the fact that μ behaves locally in the energy space and thus truncation is often a valid approximation. The matrix element of the momentum operator p αβ = ⟨α|p|β⟩, on the other hand, is related to x αβ as follows