  We study the coalescence of two bound energy eigenstates embedded in the
continuous spectrum of a real Hamiltonian $H[4]$ and the singular point
produced by this coalescence. At the singular point, the two unnormalized Jost
eigenfunctions are no longer linearly independent but coalesce to give rise to
a bound state eigenfunction embedded in the continuum. We disturb the potential
$V[4]$ by means of a truncation, this perturbation breaks the singular point in
two resonances. The phase shift shows a jump of magnitude $2\pi$ and the shape
of the cross section shows two inverted peaks, this behaviour is due to the
interference between the two nearly degenerate resonances and the background
component of the Jost function.
