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Hydrogen-atom spectrum under a minimal-length hypothesis

Sandor Benczik·Lay Nam Chang·Djordje Minic·Tatsu Takeuchi
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Abstract

The energy spectrum of the Coulomb potential with minimal length commutation relations $[X_i, P_j] = i\hbar\{δ_{ij}(1+βP^2) + β'P_iP_j\}$ is determined both numerically and perturbatively for arbitrary values of $β'/β$ and angular momenta $\ell$. The constraint on the minimal length scale from precision hydrogen spectroscopy data is of order of a few GeV$\null^{-1}$, weaker than previously claimed.

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Sandor Benczik, Lay Nam Chang, Djordje Minic, Tatsu Takeuchi. 2005-07-08. Hydrogen-atom spectrum under a minimal-length hypothesis. https://doi.org/10.1103/physreva.72.012104

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