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The multichannel scattering problem for the stationary Schr\"{o}dingerequation on a line with different thresholds at both infinities isinvestigated. The analytical structure of the Jost solutions and of thetransition matrix relating the Jost solutions as functions of the spectralparameter is described. Unitarity of the scattering matrix is proved in thegeneral case when some of the scattering channels can be closed and thethresholds can be different at left and right infinities on the line. Thesymmetry relations of the $S$-matrix are established. The condition determiningthe bound states is obtained. The asymptotics of the Jost functions and of thetransition matrix are derived for a large spectral parameter.

Multichannel scattering for the Schr\"{o}dinger equation on a line with different thresholds at both infinities