## Hydrogen atom on curved noncommutative space    [PDF]

V. G. Kupriyanov
We have calculated the hydrogen atom spectrum on curved noncommutative space defined by the commutation relations $[\hat {x}^{i},\hat{x}^{j}] =i\theta\hat{\omega}^{ij}(\hat {x})$, where $\theta$ is the parameter of noncommutativity. The external antisymmetric field which determines the noncommutativity is chosen as $\omega^{ij}(x) =\varepsilon^{ijk}{x}_{k}f({x_i}x^{i})$. In this case the rotational symmetry of the system is conserved, preserving the degeneracy of the energy spectrum. The contribution of the noncommutativity appears as a correction to the fine structure. The corresponding nonlocality is calculated: $\Delta x\Delta y \geq \frac{\theta^2}{4}m ||$, where $m$ is a magnetic quantum number.
View original: http://arxiv.org/abs/1209.6105