Noncommutative Landau problem and shifted energy levels

TL;DR

This paper explores how noncommutative geometry modifies Landau energy levels, showing that shifts can be directly derived using a Bopp shift in the generalized Hamiltonian framework.

Contribution

It introduces a straightforward method to compute shifted Landau energy levels in noncommutative space using Bopp shifts, extending traditional Landau problem analysis.

Findings

Energy levels are shifted by the noncommutative parameter.

Shifted levels can be obtained from a generalized Landau Hamiltonian.

Bopp shift provides a simple construction method.

Abstract

In this paper we discuss a Landau levels problem within the framework of noncommutative configuration space and phase space. We show that the associated energy levels are being shifted in terms of the noncommutative parameter and can be directly obtained from its associated generalized Landau Hamiltonian. A straight forward way of constructing the shifted energy levels is just via a proper defined Bopp shift applied onto the spatial and momenta operators that are used to describe the Landau levels in symmetric gauge potential.