Asymptotic Behavior of Solutions of the Nonstationary Schrödinger Equation on the Semi-Axis with a Potential Which Slowly Depends on Time

We study the asymptotic behavior of solutions of the Cauchy problem for the nonstationary Schrödinger equation on the semi-axis with a rapidly decreasing potential. The construction of the asymptotic solutions is based on the spectral expansion of the solution at a given time. This construction does not use the adiabatic theorem of scattering theory. In the highest order (as in the approach associated with the adiabatic theorem of scattering theory), the solution does not depend on the dynamics of the potential and is completely determined by the value of the potential at the zero instant of time. In this paper, we calculated power-law corrections to the leading term of the solution associated with the boundary of the continuous spectrum, which take into account the time dependence of the operator.