Abstract
The semiclassical asymptotics of the solution to the Cauchy problem for the nonstationary Schrödinger equation \(\hat{L} = -i\hbar\frac{\partial}{\partial t} - \frac{\hbar^2}{2}\Delta + \alpha \delta_{x_0},\quad \alpha \in \mathbb{R},\) with a point \(\delta\) -potential in \(\mathbb{R}^3\) is described. The initial condition is taken in the form of a rapidly oscillating wave packet with compact support contained in a ball of sufficiently small radius \(R < |x_0|\) . Explicit asymptotic formulas describing the evolution of the wave packet and its scattering by the \(\delta\) -potential are obtained. It is proved that, for the considered class of initial conditions, the scattered wave is purely outgoing.
