On semi-classical limit of nonlinear quantum scattering
On semi-classical limit of nonlinear quantum scattering
We consider the nonlinear Schrödinger equation with a short-range external potential, in a semi-classical scaling.We show that for fixed Planck constant, a complete scattering theory is available, showing that both the potential and the nonlinearity are asymptotically negligible for large time.Then, for data under the form of coherent state, we …