 0933 S. Ben Hariz ; M. Ben Salah ; H. Najar
 On the discrete spectrum of a spatial quantum waveguide with a disc window
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Feb 21, 09

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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 $\displaystyle \frac{a}{d}$.
When $a$ tends to the infinity, the asymptotic of the eigenvalue is
given.
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