The semiclassical limit on a star-graph with Kirchhoff conditions

Abstract We consider the dynamics of a quantum particle mass m on n -edges star-graph with Hamiltonian $$H_K=-(2m)^{-1}\hbar ^2 \Delta $$ H K = - ( 2 m ) 1 ? ? and Kirchhoff conditions in vertex. describe semiclassical limit evolution an initial state supported one edges close to Gaussian coherent state. define limiting classical through Liouville operator graph, obtained by means Kre?n’s theory singular perturbations self-adjoint operators. For same class states, we study wave scattering operators for couple $$(H_K,H_{D}^{\oplus })$$ , D ? , where $$H_{D}^{\oplus }$$ is Dirichlet