  The properties of open quantum systems are described well by an effective
Hamiltonian ${\cal H}$ that consists of two parts: the Hamiltonian $H$ of the
closed system with discrete eigenstates and the coupling matrix $W$ between
discrete states and continuum. The eigenvalues of ${\cal H}$ determine the
poles of the $S$ matrix. The coupling matrix elements $\tilde W_k^{cc'}$
between the eigenstates $k$ of ${\cal H}$ and the continuum may be very
different from the coupling matrix elements $W_k^{cc'}$ between the eigenstates
of $H$ and the continuum. Due to the unitarity of the $S$ matrix, the
$\TW_k^{cc'}$ depend on energy in a non-trivial manner, that conflicts with the
assumptions of some approaches to reactions in the overlapping regime. Explicit
expressions for the wave functions of the resonance states and for their phases
in the neighbourhood of, respectively, avoided level crossings in the complex
plane and double poles of the $S$ matrix are given.
