In quantum mechanics, and in particular in scattering theory, the Feshbach–Fano method, named after Herman Feshbach[1][2] and Ugo Fano,[3] separates (partitions) the resonant and the background components of the wave function and therefore of the associated quantities like cross sections or phase shift.
If one succeeds in translating the flat continuum hypothesis in a mathematical form, it is possible to generate a set of equations defining P and Q on a less arbitrary basis.
It is often supposed that the solution of this problem is trivial or at least fulfilling some standard hypotheses which allow to skip its full resolution.
is close to the real axis it gives rise to a Breit–Wigner or a Fano profile in the corresponding cross section.
Both resulting T matrices have to be added in order to obtain the T matrix corresponding to the full scattering problem :