Hydrogen-atom spectrum under a minimal-length hypothesis

Abstract

The energy spectrum of the Coulomb potential with minimal length commutation relations $[X_i,P_j]=i\hslash \{{\delta }_{ij}(1+\beta P^2)+{\beta }^{\prime }{P}_i{P}_j\}$ is determined both numerically and perturbatively for arbitrary values of ${\beta }^{\prime }/\beta$ 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.

4 pages, 3 figures, typos corrected, reference added