In the book Mathematical concepts of quantum mechanics ,Stephen J. Gustafson Israel,Michael Sigal, they say
The notion of a resonance is a key notion in quantum physics. It refers to a metastable state – i.e., to a state which behaves like a stationary (bound) state for a long time interval, but which eventually breaks up. In other words, the resonances are states of the essential 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
What is the difference between metastable states and excited states?
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