Abstract

In this paper, we obtained the expression for the noncommutative quadrupole potential and computed the second-order noncommutative quadrupole effect on the ground-state energy of the hydrogen atom. This computation was done using both the second-order perturbation theory and the exact computation using the Dalgarno–Lewis method. As a result, a sum rule was obtained and shown to be consistent with the quadrupole sum rule derived by Bell.

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