Resonances for Hamiltonians with a delta perturbation in one dimension

We analyse the existence of almost exponentially decaying states associated with quasi-stationary states of the Hamiltonian H omega = -(dx2)/(d2) + omega delta(a) defined on L-2 (R+), where delta(a) is the repulsive delta potential. We use Krein's fon-nula to study the time evolution of the system defined by H,,,. In this paper we find that the quasi-stationary states in the infinite limit omega -> infinity, decay almost exponentially; this fact can be explained physically due to the existence of resonances.