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

An algebraic method for solving the inverse problem of quantum scattering theory