Fano Resonances

Abstract

All the solvable models that we have seen in previous chapters lead to continuum spectra for unbound particles and discrete spectra for bound states; for example, the H atom gave us an infinity of discrete states and the electron-proton continuum. While this may be a useful first approach to the Physics of bound states, in reality, all excited states have one or several decay mechanisms. For example, the 2p level of Hydrogen is discrete, but is degenerate with a system comprising the atom in the 1s state $+$ a photon, whose energy belongs to a continuum. Including the coupling between the atom and the radiation field, we obtain a finite lifetime and a width to all excited states, in accord with the uncertainty principle. But the excited levels do not simply broaden. They acquire structure when coupled to continua. One can add many more examples of resonances to those enlisted in Sect. 11.6.

Quantum Mechanics replaces smooth trends of Classical physics by sharp leaps, but the discrete energy levels are always resonant. This means that we have missed something general and important up to now.