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Shyu for their programs and assistance in the numerical integration of Eq. (5). Keil (Ref. 2) has noted the relationship between S and a Bessel function of the second kind, of imaginary argument. , Phys. Rev. 133, A1717 (1964). 3M. Stevens and M. Menes, private communication of preliminary results, to be published.Eigenvalues of finite translations are used for specifying a complete set of states in quantum mechanics. A derivation of these states is given and they are shown to be very useful in solid-state physics.

Equations are derived for determining magneto-optic coefficients in multilayer systems with arbitrary directions of their magnetizations. The equations are cast in a matrix form that is suitable for numerical simulations. This establishes a framework for calculating the Kerr and Faraday effects for a multilayer system in much the same way as has been applied previously to the bulk. Numeri-0 cal Kerr results are presented for the following systems: bulk Fe, an overlayer of 50 A of Fe on Au, and for an Fe/Au superlattice for different directions of the magnetization and different angles of incidence.