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Quantum spacetime fluctuations: Lamb Shift and hyperfine structure of the hydrogen atom

We consider the consequences of the presence of metric fluctuations upon the properties of a hydrogen atom. Particularly, we introduce these metric fluctuations in the corresponding effective Schroedinger equation and deduce the modifications that they entail upon the hyperfine structure related to a hydrogen atom. We will find the change that these effects imply for the ground state energy of the system and obtain a bound for its size comparing our theoretical predictions against the experimental uncertainty reported in the literature. In addition, we analyze the corresponding Lamb shift effect emerging from these fluctuations of spacetime. Once again, we will set a bound to these oscillations resorting to the current experimental outcomes