  The spectroscopic properties of an open quantum system are determined by the
eigenvalues and eigenfunctions of an effective Hamiltonian H consisting of the
Hamiltonian H_0 of the corresponding closed system and a non-Hermitian
correction term W arising from the interaction via the continuum of decay
channels. The eigenvalues E_R of H are complex. They are the poles of the
S-matrix and provide both the energies and widths of the states. We illustrate
the interplay between Re(H) and Im(H) by means of the different interference
phenomena between two neighboured resonance states. Level repulsion along the
real axis appears if the interaction is caused mainly by Re(H) while a
bifurcation of the widths appears if the interaction occurs mainly due to
Im(H). We then calculate the poles of the S-matrix and the corresponding
wavefunctions for a rectangular microwave resonator with a scatter as a
function of the area of the resonator as well as of the degree of opening to a
guide. The calculations are performed by using the method of exterior complex
scaling. Re(W) and Im(W) cause changes in the structure of the wavefunctions
which are permanent, as a rule. At full opening to the lead, short-lived
collective states are formed together with long-lived trapped states. The
wavefunctions of the short-lived states at full opening to the lead are very
different from those at small opening. The resonance picture obtained from the
microwave resonator shows all the characteristic features known from the study
of many-body systems in spite of the absence of two-body forces. The poles of
the S-matrix determine the conductance of the resonator. Effects arising from
the interplay between resonance trapping and level repulsion along the real
axis are not involved in the statistical theory.
