  The description of bumps in scattering cross-sections by Breit-Wigner
amplitudes led in the framework of the mathematical Physics to its formulation
as the so-called Resonance-Decay Problem. It consists of a spectraltheoretical
component and the connection of this component with the construction of
decaying states. First the note quotes a solution for scattering systems, where
the absolutely continuous parts of the Hamiltonians are semi-bounded and the
scattering matrix is holomorphic in the upper half plane. This result uses the
approach developed by Lax and Phillips, where the energy scale is extended to
the whole real axis. The relationship of the spectraltheoretical part of its
solution and corresponding solutions obtained by other approaches is explained
in the case of the Friedrichs model. A No-Go theorem shows the impossibility of
the total solution within the specific framework of non-relativistic quantum
mechanics. This points to the importance of the Lax-Phillips approach. At last,
a solution is presented, where the scattering matrix is meromorphic in the
upper half plane.
