Electric-dipole selection rules for hydrogen

For the $z$ component of position,requires $\Delta m=0$ and $\Delta \ell =\pm 1$. The first condition follows from $[L_z,z]=0$; the second follows from the vector-operator angular-momentum relation together with odd parity.

The even, spherically symmetric hydrogen ground state has no permanent electric dipole, so a uniform electric field gives no first-order energy shift. Odd-parity excited states mix in at second order, yielding a negative shift quadratic in the field.