Solution of Mathieu's Type of Secular Equations

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Abstract
A discussion is given for the general solution of a secular equation with all other matrix elements equal to zero except Hii , Hi i+h , and Hi+h i . Both the eigenvalue and the amplitudes of the corresponding eigenfunction are expressed in terms of continued fractions of the matrix elements. A solution of Mathieu equation is used as an example to compare the present method with other methods.

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