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摘要
In the context of complex WKB analysis, we discuss a one-dimensional Schrodinger equation -h(2)partial derivative(2)(x) f(x, h) +[Q(x) + hQ(1)(x, h)] f(x, h)=0, h -> 0, where Q(x), Q(1)(x, h) are analytic near the origin x = 0, Q(0) = 0, and Q(1)(x, h) is a factorially divergent power series in h. We show that there is a change of independent variable y = y(x, h), analytic near x = 0 and factorially divergent with respect to h, that transforms the above Schrodinger equation to a canonical form. The proof goes by reduction to a mildly nonlinear equation on y(x, h) and by solving it using an appropriately modified Newton's method of tangents.
- 出版日期2014-12-15
