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Hydrogen-atom spectrum under a minimal-length hypothesis
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abstract
The energy spectrum of the Coulomb potential with minimal length commutation relations $[X_i, P_j] = i\hbar\{\delta_{ij}(1+\beta P^2) + \beta'P_iP_j\}$ is determined both numerically and perturbatively for arbitrary values of $\beta'/\beta$ 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.
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Cited by 1 Pith paper
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Deformed algebraic structure of angular momenta: GUP perspective
The paper derives GUP-modified angular momentum and hydrogen energy shifts, but the central commutator step is mathematically unjustified.
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