A resonance is a quantum state* which mean energy lies above the fragmentation threshold of a system and is associated with
This classification makes sense only if the lifetimes of the resonances are not larger than the typical vibrational time of the system. In this case (overlapping resonances), the situation is much less clear (see J. Chem. Phys. 116 (2002) 8318-8326, J. Chem. Phys. 104 (1996) 2222-2236, or J. Chem. Phys. 103 (1995) 4524-4537)
The lecture presented at the European Winter School on Theoretical Method for electron and positron induced chemistry presents an introduction to the resonance theory (click here or here).
I highly recommend the following link. You will find there a nice pedagogical introduction to the concepts of resonances and resonance particle.
If you are looking for a simple and general approach to the concept of resonance please look at this link or this link.
If you are interested in the relationship between classical and quantum resonances please have a look at Marshall Burns' homepage.
* To make a long story short : This quantum state is not necessarily normalized. It is normalized in the Feshbach-Fano approach but not in the Siegert-Gamow one. In the case its mean energy is complex, the position of the resonance is the real part of its mean energy and the half width of the resonance is its imaginary part.
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