Dual-channel scattering problem in the cavity-like potential

Abstract

We discuss one-dimensional dual-channel barrier scattering with a cavity-like structure in terms of a time-independent problem. Our model assumes that the channels interact with each other only through the cavity-like structure. The model is capable of describing the essential physics of resonant scattering such that electromagnetically induced transparency and Fano-resonance type lineshapes appear in the spectrum. In this paper, we give a complete analytical solution of the spectrum. In addition, using approximate solutions, we show how the spectrum is explained by the simplified resonant condition and appearance of zero points. The results can be checked by simple numerical calculations, making this problem suitable as a teaching aid for beginners.