# Covariant Quantum-Mechanical Scattering via Stueckelberg-Horwitz-Piron Theory

## TL;DR

This paper develops a covariant quantum mechanical scattering framework using Stueckelberg-Horwitz-Piron theory, analyzing wave functions around charged black holes and revealing charge-dependent scattering behaviors.

## Contribution

It introduces a covariant quantum scattering approach on curved spacetime and applies it to charged black holes, demonstrating charge influence on scattering cross sections.

## Key findings

- Wave functions asymptotically analyzed for charged black holes.
- Differential cross section depends on black hole charges.
- Method applicable to covariant quantum scattering in curved spacetime.

## Abstract

Based on the Stueckelberg-Horwitz-Piron theory of covariant quantum mechanics on curved spacetime, we solved wave equation for a charged covariant harmonic oscillator in the background of charged static spherically symmetric black hole. Using Greens functions , we found asymptotic form for the wave function in the lowest mode (s-mode) and in higher moments. It has been proven that for s-wave, in a definite range of solid angles, the differential cross section depends effectively to the magnetic and electric charges of the black hole.