LOCALIZED VIBRATIONAL-STATES ON THE EXTREMITY OF AN ISOLATED INHOMOGENEITY EXTENDING FROM THE 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 lattices of B atom s is considered to be bound. We present a calculation for the localize d vibrational states on the extremity of the chain A at the boundary a s a function of the system parameters. The chain, regarded as an isola ted inhomogeneity extending from the boundary into the bulk of the sys tem, together with the surface boundary, break the symmetry in two dim ensions. The matching method is used, and it is shown that it is neces sary to generalize the method in two dimensions in order to treat the evanescent vibrational states of the system.