## On the spectrum of the Schrodinger Operator with Aharonov-Bohm Magnetic Field in quantum waveguide with Neumann window    [PDF]

H. Najar, M. Rayssi
In a previous study \cite{n} 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 proved that such system exhibits discrete eigenvalues below the essential spectrum for any $a>0$. In the present work we study the effect of a magnetic filed of Aharonov-Bohm type when the magnetic field is turned on this system. Precisely we prove that in the presence of such magnetic filed there is some critical values of $a_0>0$, for which we have absence of the discrete spectrum for \$\displaystyle 0<\frac{a}{d}View original: http://arxiv.org/abs/1211.2343