Quantum resonances and time decay for a double-barrier model

Here we consider the time evolution of a one-dimensional quantum system with a double barrier given by a couple of two repulsive Dirac’s deltas. In such a “pedagogical” model we give, by means of the theory of quantum resonances, the explicit expression of the dominant terms of $<\psi ,e^{-itH}\varphi >$, where $H$ is the double-barrier Hamiltonian operator and where $\psi$ and $\varphi$ are two test functions.