01-43 Cruz-Sampedro J., Herbst I., Martinez-Avendano R.
Perturbations of the Wigner-von Neumann Potential Leaving the Embedded Eigenvalue Fixed (32K, Plain TeX) Jan 29, 01
Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

Abstract. \magnification=1200 \def\real{{\bf R} {\bf Abstract.} We investigate the Schr\"odinger operator $H=-d^2/dx^2+(\gamma/x)\sin \alpha x+V$, acting in $L^p(\real)$, $1\leq p<\infty$, where $\gamma \in \real \setminus\{ 0 \}$, $\alpha >0$, and $V \in L^1(\real)$. For $|\gamma|\leq 2\alpha/p$ we show that $H$ does not have positive eigenvalues. For $|\gamma|> 2\alpha/p$ we show that the set of functions $V\in L^1(\real)$, such that $H$ has a positive eigenvalue embedded in the essential spectrum $\sigma_{\rm ess}(H)=[0,\infty)$, is a smooth unbounded sub-manifold of $L^1(\real)$ of codimension one.

Files: 01-43.tex