  We derive new constraints on the zeros of Airy functions by using the
so-called quantum bouncer system to evaluate quantum-mechanical sum rules and
perform perturbation theory calculations for the Stark effect. Using
commutation and completeness relations, we show how to systematically evaluate
sums of the form $S_{p}(n) = \sum_{k \neq n} 1/(\zeta_k - zeta_n)^p$, for
natural $p > 1$, where $\zeta_n$ is the $n$-th zero of $Ai(\zeta)$.
