The Feynman Path Integral Formulation of Non-Dispersive Airy Wave Packets and their Applications to the Heavy Meson Mass Spectra and Ultra-Cold Neutrons

Abstract

Abstract
We demonstrate the non-spreading behavior of Airy wave packets utilizing the Feynman path integral formulation of a linear potential, the Airy functions’ zeros correspondence to heavy-meson mass spectroscopy, and their implications to the eigenstates of ultra-cold neutrons in Earth’s gravitational field. We derive the linear kernel, and utilize the Feynman path integral time evolution to show that Airy function wave packets are non-dispersive in free space. We then model the confining contribution to 1S - 2S heavy meson mass gaps as a 1+1D absolute linear potential and look at the correspondence of the Airy function zeros. In doing so, we predicted the confining contribution to the mass gap of heavy mesons with a good accuracy when compared to calculations performed in the light front. Furthermore, we used these Airy function solutions to model the quantum states of a neutron under Earth’s gravity. We show that the measured heights of a neutron can be modeled by the zeros of the Airy function, and compare to experimental data and predictions utilizing the WKB approximation.