Discrete representation of the spectral shift function and the multichannel $S$-matrix

A new method for solving the multichannel quantum scattering problem in a wide energy range based on the single diagonalization of the Hamiltonian matrix of the system in a finite-dimensional basis is briefly described. It has been shown that the interaction-matrix-induced shifts of the eigenvalues of the free Hamiltonian matrix in the continuous spectrum are directly related to the partial phase shifts. The two-channel scattering problem with shifted channel thresholds is considered for illustration.