The notion of a resonance is a key notion in quantum physics. It refers to metastable states — i.e., to states which behave like stationary states for long time intervals, but which eventually break up. In other words, these are states of the continuous spectrum (i.e. scattering states), which for a long time behave as if they were bound states. In fact, the notion of a bound state is an idealization: most of the states which are (taken to be) bound states in certain models, turn out to be resonance states in a more realistic description of the system.
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