Airy-Type Relativistic Matter Wave

Abstract

A new relativistic Airy-type matter wave is introduced as a solution of the kinetic energy based wave equation. The parametric solution of the related differential equation is obtained. The total energy and momentum of the relativistic particle are derived by using a Bohmian type of decomposition of the kinetic energy based equation. The acceleration of the particle is also evaluated. The behavior of the matter wave is investigated numerically.