Constraints on Airy function zeros from quantum-mechanical sum rules

M. Belloni, R. W. Robinett

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


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 Sp(n) = ∑k≠n1/(ζk - ζn)p, for natural p > 1, where -ζn is the nth zero of Ai(ζ).

Original languageEnglish (US)
Article number075203
JournalJournal of Physics A: Mathematical and Theoretical
Issue number7
StatePublished - 2009

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modeling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)


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