Localization at threshold in noncommutative space

Pulak Ranjan Giri

doi:10.1016/j.physleta.2008.06.001

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arXiv · 0801.0356

Localization at threshold in noncommutative space

Pulak Ranjan Giri

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Abstract

The ground state energy of a scale symmetric system usually does not possess any lower bound, thus making the system quantum mechanically unstable. Self-adjointness and renormalization techniques usually provide the system a scale and thus making the ground state bounded from below. We on the other hand use noncommutative quantum mechanics and exploit the noncommutative parameter Θas a scale for a scale symmetric system. The resulting Hamiltonian for the system then allows an unusual bound state at the threshold of the energy, E=0. Apart from the Hamiltonian \hat{H} we also compute the other two generators of the so(2,1) algebra, the dilation \hat{D} and the conformal generator \hat{K} in the noncommutative space. The so(2,1) algebra is not closed in the noncommutative space, but the limit Θ\to 0 smoothly goes to the so(2,1) algebra restoring the conformal symmetry. We also discuss the system for large noncommutative parameter.

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Pulak Ranjan Giri. 2008-02-07. Localization at threshold in noncommutative space. https://doi.org/10.1016/j.physleta.2008.06.001

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