# Comparing the Schr\"odinger and Dirac Descriptions of an Electron in a Uniform Magnetic Field

## TL;DR

This paper compares non-relativistic and relativistic quantum descriptions of an electron in a uniform magnetic field, highlighting differences and relativistic effects using Schrödinger and Dirac equations.

## Contribution

It provides a detailed comparison of Schrödinger and Dirac models for an electron in a magnetic field, emphasizing relativistic modifications.

## Key findings

- Relativistic effects alter the electron's behavior in a magnetic field.
- Differences between Schrödinger and Dirac descriptions are systematically analyzed.
- Relativistic phenomena impact the quantum state evolution of the electron.

## Abstract

In this article we present a detailed description of an electron in a uniform magnetic field evolving under the Schr\"odinger equation using ladder operators. Based on this analysis, we describe the same physical system using the Dirac equation, known from relativistic quantum mechanics. The main differences between these two quantum mechanical approaches are discussed and we observe specifically how the relativistic phenomena modify the description of this particular quantum system.