Landau Levels and the Issue of Gauge Invariance in Confined Spaces

Abstract

We examine the behaviour of a charged particle in a two-dimensional confining potential, in the presence of a magnetic field. The confinement serves to remove the otherwise infinite degeneracy, but additional ingredients are required to produce sensible results. We treat both circular and square geometries, and in the latter we explicitly demonstrate the gauge invariance of the energy levels and wave function amplitudes. Both bulk states and edge states are examined, and in the latter case, with sufficiently high quantum numbers we achieve significant differences in the square and circular geometries. Results are achieved using straightforward matrix mechanics, in a manner that is accessible to novices in the field.

arXiv commentnew version, sections rewritten

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• Landau Levels and the Issue of Gauge Invariance in Confined Spaces

Cited by in corpus (6)

• Landau Levels and the Issue of Gauge Invariance in Confined Spaces
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• First-quantized eigensolver for ground and excited states of electrons under a uniform magnetic field
• Algebraic Approach to Relativistic Landau Levels in the Symmetric Gauge
• Bound-state solutions for the charged Dirac oscillator in a rotating frame in the Bonnor-Melvin-Lambda spacetime