# Dirac Equation In The Curved Spacetime and Generalized Uncertainty Principle: A fundamental quantum mechanical approach with energy dependent potentials

## TL;DR

This paper explores solutions to the (1+1)-dimensional Dirac equation in curved spacetime under the generalized uncertainty principle, revealing effects of minimal length and energy-dependent potentials on quantum particles in gravitational backgrounds.

## Contribution

It introduces a novel approach combining the Dirac equation with the generalized uncertainty principle and supersymmetric quantum mechanics to analyze energy-dependent metrics.

## Key findings

- Minimal length parameters influence Dirac particles in curved spacetime.
- Supersymmetric quantum mechanics helps derive new metric functions.
- Energy-dependent potentials can be extended to energy-dependent metrics.

## Abstract

In this work, we have obtained the solutions of the (1 + 1) dimensional Dirac equation on a gravitational background within the generalized uncertainty principle. We have shown that how minimal length parameters effect the Dirac particle in a spacetime described by conformally flat metric. Also, supersymmetric quantum mechanics is used both to factorize the Dirac Hamiltonians and obtain new metric functions. Finally, it is observed that the energy dependent potentials may be extended to the energy dependent metric functions.