On helmholtz problem for plane periodic structures

摘要

the plane Helmholtz problem of the periodic disc structure with the phase shifts conditions of the solution along the basis lattice vectors and the Direchlet conditions on the disc boundaries is reduced to the integral equations for the simple layer potentials of the lattice Green function on the boundary of one disc. Some numerical results for the quantum desymmetrized Sinai's billiard and the general quantum rectangular Billiard are presented.