Abstract In this article, we revisit the observability of the Schrödinger equation on the two‐dimensional torus. In contrast to the Schrödinger operator with a purely electric potential, for which any nonempty open set guarantees observability, the presence of a magnetic potential introduces an additional obstruction. We establish a sufficient and almost necessary geometric condition for the observability of electromagnetic Schrödinger operators. This condition incorporates the magnetic potential, which can also be characterized by a geometric control condition for the corresponding magnetic field.
Balc'h et al. (Fri,) studied this question.
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