A relation between the eigenvalues of an effective Hamilton operator and the
poles of the S matrix is derived which holds for isolated as well as for
overlapping resonance states. The system may be a many-particle quantum system
with two-body forces between the constituents or it may be a quantum billiard
without any two-body forces. Avoided crossings of discrete states as well as of
resonance states are traced back to the existence of branch points in the
complex plane. Under certain conditions, these branch points appear as double
poles of the S matrix. They influence the dynamics of open as well as of
closed quantum systems. The dynamics of the two-level system is studied in
detail analytically as well as numerically.Comment: 21 pages 7 figure
