The semi-classical limit with a delta-prime potential

We consider the quantum evolution [Formula: see text] of a Gaussian coherent state localized close to classical text], where denotes self-adjoint realization formal Hamiltonian with derivative Dirac’s delta distribution at and real parameter. show that in semi-classical limit such can be approximated (with respect text]-norm, uniformly for any away from collision time) by is suitable extension restriction ([Formula: times) generator free dynamics. While operator here utilized similar one appearing our previous work [C. Cacciapuoti, D. Fermi A. Posilicano, The potential, Ann. Mat. Pura Appl. 200 (2021) 453–489], present case approximation gives smaller error: it order whereas turns out potential. also provide results both wave scattering operators.