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

A one-dimensional non-stationary 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 in turn. We study a solution that is close at some moment to an eigenfunction the stationary operator. As long as the corresponding eigenvalue exists, this solution is localized inside the potential well. In our previous paper, we described its delocalization happening when the eigenvalue disappears. This paper describes the effects that occur after the delocalization.