  We study the well-known Friedrichs model, in which a discrete state is
coupled to a continuum state. By examining the pole behaviors of the Friedrichs
model in a specific form factor thoroughly, we find that, in general, when the
bare discrete state is below the threshold of the continuum state, there should
also be a virtual-state pole accompanying the bound-state pole originating from
the bare discrete state as the coupling is turned on. There are also other
second-sheet poles originating from the singularities of the form factor. We
give a general argument for the existence of these two kinds of states. As the
coupling is increased to a certain value, the second-sheet poles may merge and
become higher-order poles. We then discuss the completeness relations
incorporating bound states, virtual states, and resonant states corresponding
to higher-order poles.
