We investigate the dynamical effects of non-stationary boundaries on the stability of a quantum Hamiltonian system described by a periodic family of Sturm-Liouville operators, a Schrodinger equation defined on
as well as boundary conditions at modeled by the -periodic function . Employing extended Hilbert space methods, stability conditions for the spectra of the evolution operators to the families under perturbations induced by variations of boundary oscillations, respectively conditions, are derived. In particular, it is shown that the existence of a pure point finitely degenerate realization implies pure point for all , whereas in case of infinitely degenerate the existence of , respectively , is possible.
Submitted December 18, 1997. Published July 17, 1998.
Math Subject Classification: 35P05, 81Q10.
Key Words: Stability of dense point spectra, boundary induced perturbations, Krein's resolvent formula.
Show me the PDF file (235 KB), TEX file, and other files for this article.