An approximate method for solving the inverse scattering problem with fixed-energy data

Assume that the potential q(r), r > 0, is known for r ≥ a > 0, and the phase shifts δl(k) are known at a fixed energy, that is at a fixed k, for l = 0, 1, 2, . . . . The inverse scattering problem is: find q(r) on the interval 0≤ r ≤ a, given the above data. A very simple approximate numerical method is proposed for solving this inverse problem. The method consists in reduction of this problem to a moment problem for q(r) on the interval r ∈ [0, a]. This moment problem can be solved numerically.