An Improvement of the WKB Method in the Presence of Turning Points and the Asymptotic Solutions of a Class of Hill Equations

概要

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A method of successive approximation, which is essentially a modified form of the WKB method, is developed to express, for large values of parameter h, the asymptotic solutions of a linear second order differential equation d^2y/(dx^2)-(λ+h^2f(x))y = 0, in the region where the zeros of the coefficient of y are present. Several simple cases are treated as elementary examples. It is shown that a class of Hill equations is included in the category to which our method is applicable, and that their uniformly valid asymptotic solutions can be expressed in terms of Mathieu functions. The locally valid expressions are also given by means of the above method.
社団法人日本物理学会の論文
1959-12-05