  In the framework of the rigged Hilbert space, unstable quantum systems
associated with first order poles of the analytically continued S-matrix can be
described by Gamow vectors which are generalized vectors with exponential decay
and a Breit-Wigner energy distribution. This mathematical formalism can be
generalized to quasistationary systems associated with higher order poles of
the S-matrix, which leads to a set of Gamow vectors of higher order with a
non-exponential time evolution. One can define a state operator from the set of
higher order Gamow vectors which obeys the exponential decay law. We shall
discuss to what extend the requirement of an exponential time evolution
determines the form of the state operator for a quasistationary microphysical
system associated with a higher order pole of the S-matrix.
