Hydrogen atom on curved noncommutative space

Abstract

We have calculated the hydrogen atom spectrum on curved noncommutative space defined by the commutation relations $\left[{\hat{x}}^i,{\hat{x}}^j\right]=i\theta {\hat{\omega }}^{ij}\left(\hat{x}\right)$, where $\theta$ is the parameter of noncommutativity. The external antisymmetric field which determines the noncommutativity is chosen as ${\omega }^{ij}(x)={\epsilon }^{ijk}{x}_{k}f\left(x_i{x}^i\right)$. 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: $\Delta x\Delta y\ge \frac{{\theta }^2}{4}|m⟨f^2⟩|$, where $m$ is a magnetic quantum number.

References in corpus (7)

• Position-dependent noncommutativity in quantum mechanics
• Magnetic-Dipole Spin Effects in Noncommutative Quantum Mechanics
• Noncommutativity due to spin
• Star products made (somewhat) easier
• Dynamics of a Dirac Fermion in the presence of spin noncommutativity
• Twist Deformation of Rotationally Invariant Quantum Mechanics
• Noncommutativity in (2+1)-dimensions and the Lorentz group

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