  We present a new algebraic method for solving the inverse problem of quantum
scattering theory based on the Marchenko theory. We applied a triangular wave
set for the Marchenko equation kernel expansion in a separable form. The
separable form allows a reduction of the Marchenko equation to a system of
linear equations. For the zero orbital angular momentum, a linear expression of
the kernel expansion coefficients is obtained in terms of the Fourier series
coefficients of a function depending on the momentum q and determined by the
scattering data on the finite range of q.
