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We demonstrate an explicit numerical method for accurate calculation ofthe analytic continuation of the scattering matrix, describing the multichannelscattering by a quantum well, to the unphysical region of complexvalues of the energy. Results of calculations show that one or severalpoles of the S-matrix exist, corresponding to the over-barrier resonantstates that are critical for the effect of the absolute reflection at scatteringof the heavy hole by a quantum well in the energy range where only theheavy hole may propagate over barriers in a quantum-well structure.Light- and heavy-hole states are described by the Luttinger Hamiltonianmatrix. The qualitative behaviour of the over-barrier scattering andresonant states is the same at variation of the shape of the quantum-wellpotential, however lifetimes of resonant states depend drastically on theshape and depth of a quantum well

The over-barrier resonant states and multi-channel scattering by a quantum well