Expansions in Breit-Wigner amplitudes and biorthogonal functions

The problem of finding the expansion coefficients for a finite superposition of Breit-Wigner amplitudes is discussed. Since such amplitudes are not mutually orthogonal, another set of functions orthogonal to the Breit-Wigner functions are computed. Advantages and disadvantages of this biorthogonal set of functions are compared with conventional orthogonal functions and, in particular, the problem of reading off expansion coefficients when the modulus squared of the amplitude is known—rather than the amplitude itself—is discussed.