Michelangeli, Alessandro2006-04-182011-09-072006-04-182011-09-072006-04-18https://openscience.sissa.it/handle/1963/1819"It has a flavour of Mathematical Physics..."With these words, just few years ago, prof. Di Giacomo used to introduce the topic of the Born approximation within a nonrelativistic potential theory, in his `oversize' course of Theoretical Physics in Pisa. Something maybe too fictitious inside the formal theory of the scattering he was teaching us at that point of the course. Now that I'm (studying to become) a Mathematical Physicist indeed, dealing with such an `exotic tasting' topic, those words come back to the mind, into a new perspective. Here the very recent problem of the rigorous derivation of the cubic nonlinear Schrödinger equation (the Gross-Pitaevskiî equation) is reviewed and discussed, with respect to the role of the Born approximation that one ends up with in an appropriate scaling limit154961 bytesapplication/pdfen-USPreprint