STARK EFFECT

The application of external uniform electric field as a perturbation to an atom causes splitting of the degenerate energy levels and is called the Stark effect. The perturbation due to external electric field is given as follows:

Consider the previous perturbation to the ground state of a hydrogen atom. The ground state has the following wave function (n = 1, l = 0, m = 0):

According to first-order perturbation to energy:

Thus, the previous perturbation to the ground state does not have first-order correction to the energy.
What about the perturbation of n = 2 energy level of the hydrogen atom?
To answer the question, we need to understand parity of a wave function.