01209nas a2200097 4500008004300000245009800043210006900141520083600210100002901046856003601075 2006 en_Ud 00aBorn approximation in the problem of the rigorous derivation of the Gross-Pitaevskii equation0 aBorn approximation in the problem of the rigorous derivation of 3 a\\\"It has a flavour of Mathematical Physics...\\\"With these words, just few years ago, prof. Di Giacomo\\nused 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\\nthe 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 limit1 aMichelangeli, Alessandro uhttp://hdl.handle.net/1963/1819