  We show that the quantization of a simple damped system leads to a
self-adjoint Hamiltonian with a family of complex generalized eigenvalues. It
turns out that they correspond to the poles of energy eigenvectors when
continued to the complex energy plane. Therefore, the corresponding generalized
eigenvectors may be interpreted as resonant states. We show that resonant
states are responsible for the irreversible quantum dynamics of our simple
model.
