Аннотация:
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.
Образец цитирования:
A. A. Fedotov, “Adiabatic evolution generated by a one-dimensional Schrödinger operator with decreasing number of eigenvalues”, Math. Notes, 116:4 (2024), 804–830