Is the X(3872) a molecule?

Because of the controversial X(3872) meson's very close proximity to the $D^0\barD^*0$ threshold, this charmonium-like resonance is often considered a meson-meson molecule. However, a molecular wave function must be essentially of a meson-meson type, viz. $D^0\barD^*0$ in this case, with no other significant components. We address this issue by employing a simple two-channel Schrödinger model, in which the $J^PC=1^++$ $c\barc$ and $D^0\barD^*0$ channels can communicate via the $^3P_0$ mechanism, mimicked by string breaking at a sharp distance $a$. Thus, wave functions and their probabilities are computed, for different bound-state pole positions approaching the $D^0\barD^*0$ threshold from below. We conclude that at the PDG X(3872) mass and for reasonable values of $a$, viz. 2.0 to 3.0 GeV$^-1$, the $c\barc$ component remains quite substantial and certainly not negligible, despite accounting for only about 6 to 10% of the total wave-function probability, owing to the naturally long tail of the $D^0\barD^*0$ component.