In order to obtain a non-zero matrix V int for systems with an inversion center it is necessary that some of the unperturbed functions ψ ψ i 0 have opposite parity (obtain plus and minus under inversion), because only functions of opposite parity give non-vanishing matrix elements. Degenerate zeroth-order states of opposite parity occur for excited hydrogen-like (one-electron) atoms or Rydberg states. Neglecting fine-structure effects, such a state with the principal quantum number n is n -fold degenerate and n 2 = ∑ ∑ ℓ ℓ = 0 n − − 1 ( 2 ℓ ℓ + 1 ) , where ℓ ℓ is the azimuthal (angular momentum) quantum number. For instance, the excited n = 4 state contains the following ℓ ℓ states, 16 = 1 + 3 + 5 + 7 ⟹ ⟹ n = 4 contains s ⊕ ⊕ p ⊕ ⊕ d ⊕ ⊕ f . The one-electron states with even ℓ ℓ are even under parity, while those with odd ℓ ℓ are odd under parity. Hence hydrogen-like atoms with n >1 show first-order Stark effect.