G.F. Dell'Antonio, R. Figari, A. Teta
Schr\"{o}dinger Equation with Moving Point Interactions in Three
Dimensions.
(36K, LaTex)

ABSTRACT.  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 to the singular character of the
time-dependent interaction, the corresponding Schr\"{o}dinger equation
does not  have solutions in a strong sense and, moreover,
standard perturbation techniques cannot be used. Here we prove that, 
for smooth initial data,  there is a unique weak solution by reducing the
problem to the solution of a Volterra integral equation involving only the
time variable. It is also shown  that the evolution operator   uniquely
extends to a   unitary operator in $L^{2}(R^{3})$.