Exact form of Green functions for segmented potentials

We derive the exact Green functions for segmented potentials, i.e. for potentials of the form V(x) = Sigma(j=1)(N) V-(j)(x), where each V-(j)(x) has compact support. The expressions depend explicitly on the wavefunctions' quantum amplitudes (e.g. transmission and reflection coefficients) for the individual V-(j)'s. We also show that the exact Green functions are in fact generalizations of the usual semiclassical formula. Finally, the possibility of applying the method to a general potential is briefly discussed.