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On the Embedded Eigenvalues and Dense Point Spectrum of the Stark‐Like Hamiltonians by Sergei N. Naboko; Alexander B. Pushnitski is a Mathematics article available to read on EtoBox.

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## Abstract The point spectrum lying on the essential spectrum is investigated for the one‐dimensional Schrödinger operator \documentclass{article}\pagestyle{empty}\begin{document}$ \- \frac{{d^2 }}{{dx^2 }} + q(x) $\end{document} with decaying potential __q__, and weakly perturbed Stark‐like operator \documentclass{article}\pagestyle{empty}\begin{document}$ - \frac{{d^2 }}{{dx^2 }} - \left| x \right|^\alpha {\rm sign }x + q(x). $\end{document} An elementary constructive technique is developed to obtain various results concerning embedded eigenvalues of Schrödinger operators. In Section 3 a constructive example of the Stark ‐ like operator with the potential __q__ decaying slightly slowlier than o(1/|x|^1‐α/2^)and dense point spectrum on the whole real axis is presented.

Who reads On the Embedded Eigenvalues and Dense Point Spectrum of the Stark‐Like Hamiltonians?

Author

Sergei N. Naboko; Alexander B. Pushnitski

Publisher

John Wiley and Sons; Wiley (John Wiley & Sons); Wiley - V C H Verlag GmbbH & Co.; Wiley (ISSN 0025-584X)

Published

1997

Language

EN

Field

Mathematics (Physical Sciences)