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 \(\frac{a}{d}\). When a tends to the infinity, the asymptotic of the eigenvalue is given.
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Najar, H., Hariz, S.B. & Salah, M.B. On the Discrete Spectrum of a Spatial Quantum Waveguide with a Disc Window. Math Phys Anal Geom 13, 19–28 (2010). https://doi.org/10.1007/s11040-009-9064-0
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DOI: https://doi.org/10.1007/s11040-009-9064-0