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Energy-Time Uncertainty Relation for Absorbing Detectors

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We prove an uncertainty relation for energy and arrival time, where the arrival of a particle at a detector is modeled by an absorbing term added to the Hamiltonian. In this well-known scheme the probability for the particle's arrival at the counter is identified with the loss of normalization for an initial wave packet. The result is obtained under the sole assumption that the absorbing term vanishes on the initial wave function. Nearly minimal uncertainty can be achieved in a two-level system.