Schrödinger equation of a particle in a uniformly accelerated frame and the possibility of a new kind of quanta

Abstract

In this article we have developed a formalism to obtain the Schrödinger 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 Schrödinger 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.

Some theoretical aspects of quantum mechanical equations in Rindler space

“…We have discussed the physical significance of the solutions. To the best of our knowledge such studies have not been done before, except some preliminary studies by our group [10,11]. For the sake of completeness we have also discussed two of our already reported works.…”

Hydrogen atom wave function and eigen energy in the Rindler space

“…The first step is to find the hydrogen's Schrodinger equation in the Rindler spacetime. A free particle's Schrodinger equation has been studied for a while and it has been found that there could be a new type of quanta in the Rindler spacetime [20,21]. We extend the study to a scalar field particle which is bounded by the atom's nucleus.…”

The Propagation of de Broglie Waves in Rindler Space

“…The space is called the Rindler space [3]. In some very recent published articles we have reported the formalisms to obtain the stationary state solutions for the Schrödinger equation in Rindler space [4,5] and predicted a new kind of quanta, which is named as COSMIC PHONON by us.…”

“…The single particle Hamiltonian in Rindler space is found to be non-Hermitian. However, it is P T -symmetric [4,5]. As a consequence the energy eigen values or eigen spectrum are found to be real in nature [6] (see also [4,7] Recently we have developed an exact formalism to obtain the solutions for the relativistic version of single particle quantum mechanical equations in Rindler space [7].…”