On the first solution of a long standing problem: Uniqueness of the phaseless quantum inverse scattering problem in 3-d

After publishing his recent paper in SIAM J. Appl. Math. 74, 392–410, 2014 the author has realized that actually he has addressed in that paper, for the first time, a long standing open question being unaware about this. This question is about the uniqueness of a 3-d inverse scattering problem without the phase information. Thus, it makes sense in the current paper to explicitly make the latter statement and to formulate corresponding uniqueness theorems.