Abstract
The quasi-one-dimensional scattering of a quantum particle on the two-dimensional δ-potential is considered. Analytical expressions for multi-channel transmission tn and reflection rn amplitudes are given. The problem is solved for the case of finite number of channels that is equal to N when the particle is incident on the potential while moving in l channel. The case of three-channel scattering was examined in details. As was shown within the frameworks of this problem, the “overpopulation” of particles in the second and third channels occurs when k2 → 0 and k3 → 0. The location points of δ-potential that provide the complete “overpopulation” of channels were also obtained.
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