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An example of full solution of the inverse scattering problem on the half line (from 0 to ∞) is presented. For this purpose, a simple analytically solvable model system (Morse potential) is used, which is expected to be a reasonable approximation to a real potential. First one calculates all spectral characteristics for the fixed model system. This way one gets all the necessary input data (otherwise unobtainable) to implement powerful methods of the inverse scattering theory. In this paper,doi:10.3176/proc.2016.3.07 fatcat:3ltrislyargc3fjtdrtojuj6aq