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

我们考虑哈密​​顿量\（H_K =-（2m）^ {-1} \ hbar ^ 2 \ Delta \）和基尔霍夫条件的n边缘星图上质量为m的量子粒子的动力学。我们描述了在边缘之一上且接近于高斯相干态的初始态的量子演化的半经典极限。我们通过图上的Liouville算子定义了极限经典动力学，该算子是通过Kreĭn自伴算子的奇摄动理论获得的。对于同一类初始状态，我们研究了\（（H_K，H_ {D} ^ {\ oplus}）\）对的波动和散射算子的半经典极限，其中\（H_ {D} ^ {\ oplus} \） 是在顶点具有Dirichlet条件的哈密顿量。