On the discrete spectrum of a spatial quantum waveguide with a disc window
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2009
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| _version_ | 1866914312253079552 |
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| author | Hariz, S. Ben Salah, M. Ben Najar, H. |
| author_facet | Hariz, S. Ben Salah, M. Ben Najar, H. |
| contents | In this study we investigate the bound states of the Hamiltonian describing a quantum particle living on three dimensional straight strip of width $d$. We impose the Neumann boundary condition on a disc window of radius $a$ and Dirichlet boundary conditions on the remained part of the boundary of the strip. We prove that such system exhibits discrete eigenvalues below the essential spectrum for any $a>0$. We give also a numeric estimation of the number of discrete eigenvalue as a function of $\displaystyle \frac{a}{d}$. When $a$ tends to the infinity, the asymptotic of the eigenvalue is given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_0902_3731 |
| institution | arXiv |
| publishDate | 2009 |
| record_format | arxiv |
| spellingShingle | On the discrete spectrum of a spatial quantum waveguide with a disc window Hariz, S. Ben Salah, M. Ben Najar, H. Spectral Theory 81Q10, 47B80, 81Q15 In this study we investigate the bound states of the Hamiltonian describing a quantum particle living on three dimensional straight strip of width $d$. We impose the Neumann boundary condition on a disc window of radius $a$ and Dirichlet boundary conditions on the remained part of the boundary of the strip. We prove that such system exhibits discrete eigenvalues below the essential spectrum for any $a>0$. We give also a numeric estimation of the number of discrete eigenvalue as a function of $\displaystyle \frac{a}{d}$. When $a$ tends to the infinity, the asymptotic of the eigenvalue is given. |
| title | On the discrete spectrum of a spatial quantum waveguide with a disc window |
| topic | Spectral Theory 81Q10, 47B80, 81Q15 |
| url | https://arxiv.org/abs/0902.3731 |