On Quantum Wave Package Propagation through Potential Barriers

We consider one-dimensional wave package propagation through potential barriers. We test several approaches to obtain wave package transmission coefficients - by direct numeric solution of the time-dependent Schrӧdinger equation with step and rectangular barrier potentials, usage of the spectral decomposition of the propagator. We also rigorously derive earlier propose an asymptotic formula, that can be used for calculation of the transmission coefficient. The formula produces accurate results and is much easier applicable then other considered approaches