On the homogenization of Schrodinger operator in a strip with frequent alternation of boundary conditions

We consider a planar quantum waveguide with frequent alternation type of boundary conditions. The waveguide is modeled by a planar strip. On its lower boundary we impose frequent alternation of Dirichlet and Neumann boundary conditions. As the operator we choose the Laplacian with a real potential. We study the case when the homogenized operator has the Dirichlet condition instead of the alternating ones.We prove the uniform resolvent convergence and obtain the estimates for the rate of convergence.