Abstract:
We study a one-dimensional nonstationary Schrödinger equation
with a potential slowly depending on time. The corresponding
stationary operator depends on time as on a parameter. It has finitely many negative eigenvalues and absolutely continuous
spectrum filling
$[0,+\infty)$.
The eigenvalues move with time
to the edge of the continuous spectrum and, having reached it,
disappear one after another. We describe the asymptotic behavior of a solution
close at some moment to an eigenfunction of the stationary operator, and,
in particular, the phenomena occurring when the corresponding eigenvalue
approaches the absolutely continuous spectrum and disappears.
Citation:
A. A. Fedotov, “Adiabatic evolution generated by a one-dimensional Schrödinger operator with decreasing number of eigenvalues”, Math. Notes, 116:4 (2024), 804–830