Exceptional points in the continuous spectrum of a real pseudo-Hermitian Hamiltonian and their manifestation as resonances

We study the coalescence of two bound energy eigenstates embedded in the continuous spectrum of a real pseudo-Hermitian Hamiltonian of von Neumann-Wigner type and the exceptional point produced by this coalescence. At the exceptional point, the two unnormalized Jost eigenfunctions are no longer linearly independent but coalesce to give rise to a Jordan cycle of generalized bound state eigenfunctions embedded in the continuum and a Jordan block representation of the Hamiltonian. The time evolution of the regular scattering function is unitary, while the time evolution of the generalized eigenfunctions is pseudounitary. We disturb the potential $V[4]$ by means of a truncation, this pertubation breaks the exceptional 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 resonances and the background.