  In this paper, we revisit the Stark effect of the hydrogen atom induced by a
uniform static electric field. In particular, a general formula for the
integral of associated Laguerre polynomials was derived by applying the method
for Hermite polynomials of degree n proposed in the work [Anh-Tai T.D. et al.,
2021 AIP Advances \textbf{11} 085310]. The quadratic Stark effect is obtained
by applying this formula and the time-independent non-degenerate perturbation
theory to hydrogen. Using the Siegert State method, numerical calculations are
performed and serve as data for benchmarking. The comparisons are then
illustrated for the ground and some highly excited states to provide an
insightful look at the applicable limit and precision of the quadratic Stark
effect formula for other atoms with comparable properties.
