Schr\"odinger Equation of a particle in an Uniformly Accelerated Frame and the Possibility of a New kind of Quanta

Abstract

In this article we have developed a formalism to obtain the Schr$\ddot{\rm{o}}$dinger equation for a particle in a frame undergoing an uniform acceleration in an otherwise flat Minkowski space-time geometry. We have presented an exact solution of the equation and obtained the eigenfunctions and the corresponding eigenvalues. It has been observed that the Schr$\ddot{\rm{o}}$dinger equation can be reduced to an one dimensional hydrogen atom problem. Whereas, the quantized energy levels are exactly identical with that of an one dimensional quantum harmonic oscillator. Hence considering transitions, we have predicted the existence of a new kind of quanta, which will either be emitted or absorbed if the particles get excited or de-excited respectively.