Constraints on Airy function zeros from quantum-mechanical sum rules

Details Constraints on Airy function zeros from quantum-mechanical sum rules Constraints on Airy function zeros from quantum-mechanical sum rules

2010-07-09

arxiv.org/abs/1007.1623v1

Physics

Quantum Physics

Published as J. Phys. A: Math. Theor 42, 075203 (2009) -- requires current IOP style files

Scientific paper

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 $Ai(\zeta)$.

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