Hydrogen-atom spectrum under a minimal-length hypothesis

The energy spectrum of the Coulomb potential with minimal length commutation relations $[X_i,P_j]=i\mathrm{\hslash }\{{\delta }_{ij}(1+\beta P^2)+{\beta }^{\mathrm{\prime }}{P}_i{P}_j\}$ is determined both numerically and perturbatively for arbitrary values of ${\beta }^{\mathrm{\prime }}\mathrm{/}\beta$ and angular momenta $\mathrm{\ell }$. The constraint on the minimal length scale from precision hydrogen spectroscopy data is of order of a few GeV${\text{null}}^{-1}$, weaker than previously claimed.