The Bender-Wu Analysis and the Voros Theory

To the memory of the late Professor K. Yosida
  • Takashi Aoki
  • Takahiro Kawai
  • Yoshitsugu Takei


In their pioneering work [BW], Bender and Wu presented the secular equation for anharmonic oscillators ([BW], (F.56)~(F.58) in p. 1257), which was supported by their ingenious WKB analysis. As we shall discuss in our forthcoming article, we can validate their conjecture by Voros’ epoch-making article [V]. At the same time several ideas contained in [BW] can be effectively employed to understand the Voros theory from the viewpoint of (micro)differential operators, and this is what we report here.


Holomorphic Function Formal Series Singular Part Anharmonic Oscillator Schwarzian Derivative 


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Copyright information

© Springer-Verlag Tokyo 1991

Authors and Affiliations

  • Takashi Aoki
    • 1
  • Takahiro Kawai
    • 2
  • Yoshitsugu Takei
    • 3
  1. 1.Department of Mathematics and Physics, Faculty of Science and TechnologyKinki UniversityHigashi-Osaka 577Japan
  2. 2.Research Institute for Mathematical SciencesKyoto UniversityKyoto 606Japan
  3. 3.Department of Mathematics, Faculty of ScienceKyoto UniversityKyoto 606Japan

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