ANTIBOUND STATES AND EXPONENTIALLY DECAYING STURM–LIOUVILLE POTENTIALS
We consider the Sturm–Liouville equation \renewcommand{\theequation}{1.\arabic{equation}} \begin{equation} y^{\prime\prime}(x)+\{\lambda - q(x)\}y(x) = 0\quad (0 \le x < \infty) \end{equation} with a boundary condition at $x = 0$ which can be either the Dirichlet condition \begin{equation} y(0) =...
Gespeichert in:
Veröffentlicht in: | Journal of the London Mathematical Society 2002-06, Vol.65 (3), p.624-638 |
---|---|
1. Verfasser: | |
Format: | Artikel |
Sprache: | eng |
Online-Zugang: | Volltext |
Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
Zusammenfassung: | We consider the Sturm–Liouville equation
\renewcommand{\theequation}{1.\arabic{equation}}
\begin{equation}
y^{\prime\prime}(x)+\{\lambda - q(x)\}y(x) = 0\quad (0 \le x < \infty)
\end{equation}
with a boundary condition at
$x = 0$
which can be either the Dirichlet condition
\begin{equation}
y(0) = 0
\end{equation}
or the Neumann condition
\begin{equation}
y^\prime(0) = 0.
\end{equation}
As usual,
$\lambda$
is the complex spectral parameter with
$0 \le \arg \lambda < 2\pi$
, and the potential
$q$
is real-valued and locally integrable in
$[0, \infty)$
. |
---|---|
ISSN: | 0024-6107 1469-7750 |
DOI: | 10.1112/S0024610702003216 |