Beam Models and Quantum Systems with Linear Potentials Based on Airy Functions
Beam Models and Quantum Systems with Linear Potentials Based on Airy Functions
No Thumbnail Available
Date
2026-04-09
Authors
José A. Gómez Hernández
Juan Toribio Milané
Francis L. Álvarez Paulino
Manuel L. Reyes-Cordero
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
This article provides a rigorous study of Airy functions, emphasizing their construction
by power series, their relation with Bessel functions, and their canonical integral representation. We
highlight their asymptotic properties and structural role in mathematical physics. To illustrate their
applicability, we develop three analytical models: the Euler–Bernoulli beam under self-weight, the
quantum bouncer with a linear gravitational potential, and the particle in a uniform electric field.
In each case, the quantization conditions and physical scales naturally emerge from the zeros of
the Airy function. These results confirm the central role of Airy functions in bridging differential
equations, special functions, and applied physics.
Description
Keywords
Citation
Beam Models and Quantum Systems with Linear Potentials Based on Airy Functions. (2026). Alma Mater, 1(1).