A NOVEL-APPROACH FOR THE CALCULATION OF LOCALIZED VIBRATIONAL SURFACE-STATES ON THE TIP OF AN ISOLATED LINEAR ATOMIC CHAIN EXTENDING FROM THE SURFACE BOUNDARY INTO THE BULK OF 2-DIMENSIONAL SYSTEMS

A two dimensional system consisting of a half-infinite linear chain of A atoms wedged between two quarter-infinite square lattice of B atoms is considered. We present a novel approach for the calculation of the localized vibrational states on the extremity of the chain A at the b oundary, as a function of the system force constants. The chain, regar ded as an isolated inhomogencity extending from the boundary into the bulk of the system, together with the surface boundary, break the symm etry in two dimensions. The matching method is generalized in two dime nsions in order to treat the evanescent vibrational states of this sys tem.