  We perform an analytical study of the scattering matrix and bound states in
problems with many physical coupled channels. We establish the relationship of
the couplings of the states to the different channels, obtained from the
residues of the scattering matrix at the poles, with the wave functions for the
different channels. The couplings basically reflect the value of the wave
functions around the origin in coordinate space. In the concrete case of the
X(3872) resonance, understood as a bound state of $\ddn$ and $\ddc$ (and
$c.c.$), with the $\ddn$ loosely bound, we find that the couplings to the two
channels are essentially equal leading to a state of good isospin I=0
character. This is in spite of having a probability for finding the $\ddn$
state much larger than for $\ddc$ since the loosely bound channel extends
further in space. The analytical results, obtained with exact solutions of the
Schr\"odinger equation for the wave functions, can be useful in general to
interpret results found numerically in the study of problems with unitary
coupled channels methods.
