# Quaternionic perturbation theory

## TL;DR

This paper develops a perturbation theory for systems with quaternionic potentials, analyzing their effects on quantum states like hydrogen, well, and oscillator, and comparing with relativistic effects.

## Contribution

It introduces a novel perturbation framework for quaternionic potentials in quantum mechanics, extending traditional methods to quaternionic systems.

## Key findings

- Quaternionic perturbations affect bound state energies.
- Explicit calculations for hydrogen, well, and oscillator.
- Comparison with relativistic corrections highlights differences.

## Abstract

In this paper we present a perturbation theory for constant quaternionic potentials. The effects of quaternionic perturbations are explicitly treated for bound states of hydrogen atom, infinite potential well and harmonic oscillator. Comparison with relativistic corrections is also briefly discussed.