On the surface wave arising after delocalization of a quantum particle in the course of adiabatic evolution

A one-dimensional nonstationary Schrödinger equation is studied in the adiabatic approximation. The corresponding stationary operator, which depends on time as on a parameter, has a continuous spectrum filling the positive half-line and a finite number of negative eigenvalues. Over time, the eigenvalues approach the edge of the continuous spectrum and disappear one by one. A solution is studied that is close at some moment to an eigenfunction of the stationary operator. As long as the corresponding eigenvalue exists, this solution is localized inside the potential well. In a previous paper, the authors described its delocalization happening when the eigenvalue disappears. This paper describes the effects that occur after delocalization.