The energy spectrum of the Coulomb potential with minimal length commutation relations [Xᵢ,Pⱼ]=iδᵢⱼ(1+βP²)+β^'PᵢPⱼ is determined both numerically and perturbatively for arbitrary values of β^'∕β and angular momenta . The constraint on the minimal length scale from precision hydrogen spectroscopy data is of the order of a few GeV^-1, weaker than previously claimed.
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Benczik et al. (2005) studied this question.
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