Perspectives on the Fano Resonance Formula

The general profile of a resonance, as given by Fano in 1961, is well known throughout physics. This Comment provides some of the simplest derivations of this formula, together with a discussion of subtleties in handling continuum states with regard to their normalization, orthogonality, and completeness. Inadequate appreciation of these subtleties has led to misconceptions and errors in analysis. Recent, novel applications of the Fano formula in condensed matter systems include systems with decoherence and lack of time reversal symmetry which make the resonance profile parameter complex. An ancient pond, a frog jumps in- a deep resonance. Basho [1] (1686)