Propagation in crossed electric and magnetic fields: The quantum source approach

TL;DR

This paper develops a new approach to analyze the propagation of electrons with specific energies in static electromagnetic fields, providing insights into phenomena like photodetachment and the quantum Hall effect.

Contribution

It introduces a method to obtain the Green function for energy-specific electron propagation in electromagnetic fields, which was previously difficult to access.

Findings

Derived the Green function for energy-dependent electron propagation.

Applied the method to photodetachment current in external fields.

Analyzed the quantum Hall effect in a fermionic electron gas.

Abstract

The propagation of electrons in static and uniform electromagnetic fields is a standard topic of classical electrodynamics. The Hamilton function is given by a quadratic polynomial in the positions and momenta. The corresponding quantum-mechanical problem has been analyzed in great detail and the eigenfunctions and time evolution operators are well-known. Surprisingly, the energy-dependent counterpart of the time-evolution operator, the Green function, is not easily accessible. However in many situations one is interested in the evolution of a system that started with emitted particles that carry a specific energy. In the following we present a suitable approach to study this type of matter waves arising from a localized region in space. Two applications are discussed, the photodetachment current in external fields and the quantum Hall effect in a fermionic electron gas.