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The $\star$-value Equation and Wigner Distributions in Noncommutative Heisenberg algebras

Marcos Rosenbaum·J. David Vergara
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Abstract

We consider the quantum mechanical equivalence of the Seiberg-Witten map in the context of the Weyl-Wigner-Groenewold-Moyal phase-space formalism in order to construct a quantum mechanics over noncommutative Heisenberg algebras. The formalism is then applied to the exactly soluble Landau and harmonic oscillator problems in the 2-dimensional noncommutative phase-space plane, in order to derive their correct energy spectra and corresponding Wigner distributions. We compare our results with others that have previously appeared in the literature.

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Marcos Rosenbaum, J. David Vergara. 2005-05-13. The $\star$-value Equation and Wigner Distributions in Noncommutative Heisenberg algebras. https://doi.org/10.1007/s10714-006-0251-z

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