  The resonant state expansion, a rigorous perturbation theory, recently
developed in electrodynamics, is applied to non-relativistic quantum mechanical
systems in one dimension. The method is used here for finding the resonant
states in various potentials approximated by combinations of Dirac delta
functions. The resonant state expansion is first verified for a triple quantum
well system, showing convergence to the available analytic solution as the
number of resonant states in the basis increases. The method is then applied to
multiple quantum well and barrier structures, including finite periodic
systems. Results are compared with the eigenstates in triple quantum wells and
infinite periodic potentials, revealing the nature of the resonant states in
the studied systems.
