Charged Particle System in Uniform Magnetic and Electric Fields: The Role of Galilean Transformation

TL;DR

This paper explores how Galilean transformations can simplify the analysis of charged particle systems in combined magnetic and electric fields, impacting understanding of the Hall effect and neutral systems.

Contribution

It demonstrates how Galilean transformations relate complex electromagnetic systems to simpler cases, enabling easier quantum state analysis and insights into the Hall effect and neutral systems.

Findings

Galilean transformation links systems with combined fields to magnetic-only systems.

Quantum states can be fully specified using this transformation.

Implications for understanding the Hall effect and neutral composite systems.

Abstract

Galilean transformation relates a physical system under mutually perpendicular uniform magnetic and electric fields to that under uniform magnetic field only. This allows a complete specification of quantum states in the former case in terms of those for the latter. Based on this observation, we consider the Hall effect and the behavior of a neutral composite system in the presence of uniform electromagnetic fields.