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Gauge invariant energy spectra in 2-dimensional noncommutative quantum mechanics

Mathematical Physics 2021-05-25 v2 math.MP Quantum Physics

Abstract

In this paper we consider an electron moving on a two dimensional noncommutative plane immersed in a constant magnetic field under the influence of an anisotropic harmonic potential. We work out the gauge invariant energy spectra of this system using a consistent gauge prescription proposed in \cite{nctori,gauge-wigfunc}. We also show subsequently that straightforward generalization of the Landau problem in the noncommutative setting using minimal coupling prescription as is done naively on many occasions in the literature violates gauge invariance of the energy spectra.

Keywords

Cite

@article{arxiv.2003.12662,
  title  = {Gauge invariant energy spectra in 2-dimensional noncommutative quantum mechanics},
  author = {S. Hasibul Hassan Chowdhury and Talal Ahmed Chowdhury and MD Arman Ud Duha},
  journal= {arXiv preprint arXiv:2003.12662},
  year   = {2021}
}

Comments

23 pages, 5 figures, published version, title changed, a new section (section IV) on noncommutative quantum Hall effect is added, typos corrected, concluding remarks added based on the added section, references modified