A time‐dependent Schro¨dinger equation has been solved numerically for a double‐barrier and a quantum‐well resonant tunnelling structure. Special emphasis has been paid to the system where barriers are doped specially by negative delta‐function potentials (&dgr; potentials) which broaden the widths of the resonances and in turn decrease the dwell times. The strengths of the delta functions could be such that they may form bound states in the barrier regions, but the states bound to &dgr; potentials are very shallow. Delta‐function potentials are replaced by equivalent barriers of different heights and widths which are easy to incorporate into the numerical calculation of the propagation of the wave packet, and the corresponding physical structures can be conveniently fabricated. It is found that for a certain strength of the &dgr; potential or parametric value of the equivalent barriers in the barriers of the resonant tunneling structure, there are three resonance states very close together. The square of the wave functions trapped in the well region for the states oscillates in time for a broad wave packet inkspace, whereas the wave function trapped in the whole structure decays exponentially. The oscillating part has a resemblance with the quantum beats. There are no oscillations for a narrow wave packet inkspace.