Schrodinger Equation with Moving Point Interactions in Three Dimensions

摘要: We consider the motion of a non relativistic quantum particle in R^3 subject to n point interactions which are moving on given smooth trajectories. Due singular character time-dependent interaction, corresponding Schrodinger equation does not have solutions strong sense and, moreover, standard perturbation techniques cannot be used. Here we prove that, for initial data, there is unique weak solution by reducing problem Volterra integral involving only time variable. It also shown that evolution operator uniquely extends unitary $L^{2}(R^{3})$.