On eigenvalues of the Dirac operator located on the continuous spectrum (Q2772116)
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scientific article; zbMATH DE number 1707536
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On eigenvalues of the Dirac operator located on the continuous spectrum |
scientific article; zbMATH DE number 1707536 |
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19 February 2002
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eigenvalue
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Dirac operator
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continuous spectrum
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Sturm-Liouville operator
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On eigenvalues of the Dirac operator located on the continuous spectrum (English)
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Eigenvalues of the Dirac operator of the form NEWLINE\[NEWLINE Dy\equiv\begin{pmatrix} 0&1\\ 1&0\end{pmatrix}\frac{dy}{dx} +m\begin{pmatrix} 1&0\\ 0&-1 \end{pmatrix}+\begin{pmatrix} p(x)&q(x)\\ q(x)&-p(x)\end{pmatrix} y=\lambda y NEWLINE\]NEWLINE with \(y=(y_1, y_2)\), \(y_1(0)=0\), and \(m>0\), are considered. It is proved that there exists such an operator \(D\) that has countably many eigenvalues lying on the continuous spectrum of \(D\). The functions \(p(x)\) and \(q(x)\) are constructed.
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0.9484172463417052
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