This talk presents a time-dependent semiclassical transport model for both mixed-state and coherent pure-state scattering with quantum barriers. The steady-state Schroedinger equation is solved at the quantum barrier to obtain complex scattering coefficients used to supply an interface condition that connects two classical domains. The solution in the classical regions is obtained using a semiclassical density combined using the Hamiltonian-preserving scheme at the interface. The overall cost is roughly the same as solving a classical barrier problem.
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