Constraints on Airy function zeros from quantum-mechanical sum rules

Abstract

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 $S_p(n)={\sum }_{k\ne n}1/({\zeta }_k-zet{a}_n{)}^p$, for natural $p>1$, where ${\zeta }_n$ is the $n$-th zero of $Ai(\zeta )$.

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

References in corpus (4)

• Quantum wave packet revivals
• Measurement of quantum states of neutrons in the Earth's gravitational field
• Quantum mechanical sum rules for two model systems
• Sum rules for Confining Potentials