Effects of rainbow gravity on an electron confined to a triangular well and a periodic potential

Abstract

We investigate quantum effects concerning the modification of the background via rainbow gravity on an electron. We employ the nonrelativistic approximation of the Dirac equation to analyze these effects in depth. We initially study the interaction between an electron and a uniform electric field, by exploring confinement of the particle to a triangular potential well. We find systematic alterations in the energy levels reliant on the rainbow parameter $\epsilon$. Additionally, we investigate a particle in a periodic potential resembling a ring. We also find consistent alterations in energy levels due to changes in the background via rainbow functions. As in the previously analyzed scenario, as larger the rainbow parameter the lower the obtained energy levels. These findings underscore a systematic influence of modified gravity on particle dynamics in quantum scenarios.