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In a medium in which the index of refraction varies in one space coordinate only, transform methods are convenient for reducing an inhomogeneous scalar wave equation to an ordinary differential equation in which the square of the space-dependent index of refraction appears explicitly. An iteration-variation method for obtaining approximate expressions for the dispersion relations within the medium is discussed. The ordinary differential equation is converted to an integral equation, the solution of which is begun by iteration. The individual terms in the series thereby formed, which we shall call iterates, then form the basis of a trial function for use in a variational principle. The method is illustrated by an example.

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