We consider the inverse problem of determining the time and space dependent potential of the Schr\\"odinger equation in a bounded domain of\ Rⁿ, n\≥ 2, by boundary observation of the solution over the time span. Assuming that the divergence of the magnetic potential is, we prove that the electric potential and the magnetic potential can be\\"older stably retrieved from these data, whereas stability estimates for time-dependent coefficients problems of evolution partial differential are usually of logarithmic type.
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Kian et al. (2017) studied this question.