Overlooked Degree of Freedom in Steepest Descent Method : Steepest Descent Method Corresponding to Divergence-Free WKB Method(General and Mathamatical Physics)

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概要

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• The divergence-free WKB method proposed in our previous papers (T. Hyouguchi, S. Adachi and M. Ueda, Phys. Rev. Lett. 88 (2002), 170404 and T. Hyouguchi, R. Seto, M. Ueda and S. Adachi, Ann. of Phys. 312 (2004), 177) yields a WKB wave function free from divergence for any real argument x∈R even around the classical turning point. It is expected in asymptotic analysis that any WKB method for differential equations can be translated in one-to-one manner to the corresponding steepest descent method for integrals. This paper presents newly a steepest descent method that corresponds to our divergence-free WKB method. The experience of this translation lets us notice that the key to improving the traditional steepest descent method for general integrals to become divergence-free is the choice of integration variable to express a given integral.

• 2009-12-25

著者

• ADACHI Satoshi

  Department of Energy Sciences, Tokyo Institute of Technology

• Adachi Satoshi

  Department Of Physics Tokyo Institute Of Technology

• SETO Ryohei

  Laboratoire de Physique des Solides d'Orsay, UMR8502, Universite Paris-Sud

• Seto Ryohei

  Laboratoire De Genie Chimique Universite Paul Sabatier:department Of Physical Sciences Ritsumeikan U

• HYOUGUCHI Tadanori

  Research Organization of Science and Engineering, Ritsumeikan University

• Adachi Satoshi

  Department Of Energy Sciences Tokyo Institute Of Technology

• Hyouguchi Tadanori

  Research Organization Of Science And Engineering Ritsumeikan University:department Of Applied Mathem

• Seto Ryohei

  Laboratoire De Genie Chimique Universite Paul Sabatier:department Of Physical Sciences Ritsumeikan U

• ADACHI Satoshi

  Department of Physics, Tokyo Institute of Technology

• SETO Ryohei

  Laboratoire de Physique des Solides d'Orsay, UMR8502, Universite Paris-Sud

• Hyouguchi Tadanori

  Research Organization of Science and Engineering, Ritsumeikan University:Department of Applied Mathematics and Informatics, Ryukoku University

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