Application of an inverse problem for symmetric periodic potentials

This paper gives an algorithm for constructing symmetric periodic potential q(x) of Hill's equation from given roots of Delta(lambda) - 2 = 0. The pro blem arises from synthesizing dual-mode ring electrical circuits. In the pr esented method, the discriminant Delta(lambda) of Hill's equation is determ ined from the roots of Delta(lambda) - 2 = 0 at first, and then q(x) is con structed from the roots of Delta(lambda) +/- 2 = 0 and Delta(lambda) = 0. E xamples are provided to verify the algorithm.