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

TL;DR

This paper derives the Schrödinger equation for a particle in a uniformly accelerated frame, finds exact solutions, and predicts a new type of quanta associated with transitions between energy levels.

Contribution

It introduces a formalism for the Schrödinger equation in accelerated frames and predicts a novel quantum phenomenon related to energy transitions.

Findings

Exact solutions of the Schrödinger equation in accelerated frames

Eigenvalues match those of a 1D quantum harmonic oscillator

Prediction of a new kind of quanta emitted or absorbed during transitions

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.