S. Ben Hariz ; M. Ben Salah ; H. Najar
On the discrete spectrum of a spatial quantum waveguide with a disc window
(909K, pdf)

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.