Gauge invariant energy spectra in 2-dimensional noncommutative quantum mechanics
arXiv:2003.12662 · doi:10.1016/j.aop.2021.168505
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.
arXiv comment23 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
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Cited by in corpus (4)
- On a charged spinless point particle minimally coupled to a constant magnetic field in a noncommutative plane
- Quantum simulation of quantum mechanical system with spatial noncommutativity
- Supersymmetric Quantum Mechanics on a noncommutative plane through the lens of deformation quantization
- From Bopp Shifts to Toroidal Shadows: K-Theoretic Gap Labels in Noncommutative Quantum Mechanics