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arXiv · hep-th/0010220

Non-Commutative Quantum Mechanics

J. Gamboa·M. Loewe·J. C. Rojas
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Abstract

A general non-commutative quantum mechanical system in a central potential $V=V(r)$ in two dimensions is considered. The spectrum is bounded from below and for large values of the anticommutative parameter $θ$, we find an explicit expression for the eigenvalues. In fact, any quantum mechanical system with these characteristics is equivalent to a commutative one in such a way that the interaction $V(r)$ is replaced by $V = V ({\hat H}_{HO}, {\hat L}_z)$, where ${\hat H}_{HO}$ is the hamiltonian of the two-dimensional harmonic oscillator and ${\hat L}_z$ is z- component of the angular momentum. For other finite values of $θ$ the model can be solved by using perturbation theory.

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J. Gamboa, M. Loewe, J. C. Rojas. 2001-06-14. Non-Commutative Quantum Mechanics. https://doi.org/10.1103/physrevd.64.067901

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