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Abstract: In previous work on the quantum mechanics of an atom freely falling in ageneral curved background spacetime, the metric was taken to be sufficientlyslowly varying on time scales relevant to atomic transitions that timederivatives of the metric in the vicinity of the atom could be neglected.However, when the time-dependence of the metric cannot be neglected, it wasshown that the Hamiltonian used there was not Hermitian with respect to theconserved scalar product. This Hamiltonian was obtained directly from the Diracequation in curved spacetime. This raises the paradox of how it is possible forthis Hamiltonian to be non-hermitian. Here, we show that this non-hermiticityresults from a time dependence of the position eigenstates that enter into theSchrodinger wave function, and we write the expression for the Hamiltonian thatis Hermitian for a general metric when the time-dependence of the metric is notneglected.



Autor: Xing Huang, Leonard Parker

Fuente: https://arxiv.org/







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