Constraints on Airy function zeros from quantum-mechanical sum rules

M. Belloni; R. W. Robinett

doi:10.1088/1751-8113/42/7/075203

Constraints on Airy function zeros from quantum-mechanical sum rules

M. Belloni, R. W. Robinett

Physics

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

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) = ∑_k≠n1/(ζ_k - ζ_n)^p, for natural p > 1, where -ζ_n is the nth zero of Ai(ζ).

Original language	English (US)
Article number	075203
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	42
Issue number	7
DOIs	https://doi.org/10.1088/1751-8113/42/7/075203
State	Published - 2009

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Statistics and Probability
Modeling and Simulation
Mathematical Physics
General Physics and Astronomy

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10.1088/1751-8113/42/7/075203

Cite this

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AB - 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).

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Constraints on Airy function zeros from quantum-mechanical sum rules

Abstract

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