Stark effect in quantum waveguide with Neumann window

M. Raissi

Published 2015-01-09Version 1

In this study, we investigate the bound states of the Hamiltonian describing a quantum particle living on three dimensional straight strip of width $d$ in the presence of an the electric field of constant intensity $F$ in the direction perpendicular to the electron plane. We impose 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 in the presence of such weak and strong electric field there is some critical values for which we have absence of the discrete spectrum. We give a sufficient condition for the existence of discrete eigenvalues.