The paper presents a dynamic event-triggering mechanism for the constant and the localized damped linear Schrödinger equation. The following results are tackled: the existence of solution to the closed-loop event-triggered control system; the avoidance of the Zeno behavior due to the absence of any accumulation point of the sequence of time instants and the exponential stability based on energy estimate through the observability inequality. A simulation example based on the one-dimensional Schrödinger equation is presented to validate the theoretical results.