A formula on scattering length of positive smooth measures
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- by Masayoshi Takeda PDF
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Abstract:
M. Kac studied the scattering length probabilistically and conjectured that its semi-classical limit equals the capacity of the support of the potential. This conjecture has been proved independently by Taylor, Takahashi, and Tamura. In this paper we give another simple proof by the random time-change argument for Dirichlet forms and extend the previous results to positive measure potentials.References
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Additional Information
- Masayoshi Takeda
- Affiliation: Mathematical Institute, Tohoku University, Aoba, Sendai, 980-8578, Japan
- MR Author ID: 211690
- Email: takeda@math.tohoku.ac.jp
- Received by editor(s): March 11, 2009
- Received by editor(s) in revised form: August 19, 2009
- Published electronically: December 2, 2009
- Additional Notes: The author was supported in part by Grant-in-Aid for Scientific Research (No. 18340033 (B)), Japan Society for the Promotion of Science.
- Communicated by: Richard C. Bradley
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 1491-1494
- MSC (2010): Primary 60J45, 60J55; Secondary 31C25
- DOI: https://doi.org/10.1090/S0002-9939-09-10172-7
- MathSciNet review: 2578543