Determination of Energy Levels of a Quantum Bouncing Ball with the Numerical Support of Maple Computer Program

Abstract

The dynamics of the quantum bouncing ball under the influence of gravity has been studied. The Fourier transform techniques was first used to derive the wave function (Airy function) of the time-independent Schrodinger wave equation for a linear potential in the form of the well-known Airy integral. The asymptotic dependence of the Airy function was presented. In order to obtain the numerical solution of the energy levels of the “bouncing ball”, the power series method was first used to derive the Airy function in power series form. Subsequently, the energy levels were then computed with the support of Maple Software. The results are tabulated with the WKB (Wentzel, Kramers, and Brillouin) approximation calculations.