T.A. Suslina
On the Absence of Eigenvalues of a Matrix periodic Schrödinger Operator in a Layer
Preprint series: ESI preprints

MSC:

35J10 Schrodinger operator, See also {35Pxx}

Abstract: A matrix Schr\"odinger operator
$-\Delta +{\Cal V}(\x)$ in a layer
$\R^{d-1}\times (0,T)$, $d\geq 2$, is considered.
The potential ${\Cal V}$ is
assumed to be periodic along the layer.
On the boundary we set appropriate boundary conditions.
The Dirichlet and Neumann boundary conditions,
third type condition with periodic coefficients and
quasiperiodic conditions are allowed.
It is shown that the spectrum of the corresponding operators
is free of eigenvalues. In the selfadjoint case the spectrum
is absolutely continuous.

Keywords: Schrodinger operator, periodic operator, matrix-valued potential, layer, absolutely continuous spectrum