  In this work, we present a new result which concerns the derivation of the
Green function relative to the time-independent Schrodinger equation in two
dimensional space. The system considered in this work is a quantum particle
that have an energy E and moves in an axi-symmetrical potential. Precisely, we
have assumed that the potential V(r), in which the quantum particle moves, to
be equal to zero inside a disk (radius b) and to be equal a positive constant
V0 in a crown of internal radius b and external radius a (b < a) and equal zero
outside the crown (r > a). We have explored the diffusion states regime for
which E > V0. We have used, to obtain the Green function, the continuity of the
solution and of its first derivative at r = b and r = a. We have obtained the
associate Green function showing the resonance energies (absence of the
reflected waves) for the case E > V0.
