A note on the distributions in quantum mechanical systems

In this paper, we study the distributions and affine of quantum mechanical system. Also, discuss controllability system with related question concerning minimum time needed to steer a from unitary evolution $U(0)=I$ propagator desired $U_f$. Furthermore, paper introduces description $\mathfrak{k} \oplus \mathfrak{p}$ sub-Finsler manifold its geodesics, which equivalents problem driving an arbitrary initial state target $U_f$, some illustrative examples are included. We prove that Lie group $G$ on Finsler symmetric $G/K$ can be decomposed into $KAK$.