Analytic Expression of Voros Coefficients and Its Application to WKB Connection Problem
Usually, the WKB method starts from formal solutions (WKB or Liou ville-Green solutions) expanded in powers of the Planck constant, and connects these solutions by-asymptotic matching at turning points. Voros [V] proposed a resummation prescription of these formal calculations, and argued that his results should be deeply related with Ecalle’s theory of “resurgent functions.” Further progress along that line has been made by F. Pham and his coworkers [DDP]. We report another approach based upon an idea of Olver [O].
KeywordsHarmonic Oscillator Riccati Equation Neumann Series Connection Problem Connection Formula
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