  We present in this talk a series of new results on the nature of a bound
state or resonance based on the calculation of the expectation values of the
number operators of the free particles in the state of interest. In this way, a
new universal criterion for the elementariness of a bound state emerges. In the
case of large particle wavelengths compared to the range of their interaction,
a new closed formula for the compositeness of a bound state in a two-particle
continuum is obtained. The extension of these results to resonances with
respect to the open channels can be given by making use in addition of suitable
phase-factor transformations as also reviewed here. We end with a discussion on
the $X(3872)$ as possible double- or triple-pole virtual state, which would be
the first case in particle phenomenology.
