On the Discrete Spectrum of a Spatial Quantum Waveguide with a Disc Window |
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Authors: | Hatem Najar Samir Ben Hariz and Mounir Ben Salah |
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Institution: | 1.Département de Mathématiques,ISMAI. Kairouan,Kairouan,Tunisia;2.Département de Mathématiques,Université du Maine,Le Mans,France |
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Abstract: | 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
\fracad\frac{a}{d}. When a tends to the infinity, the asymptotic of the eigenvalue is given. |
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Keywords: | |
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