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.
Original language | English |
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Pages (from-to) | 1491-1494 |
Number of pages | 4 |
Journal | Proceedings of the American Mathematical Society |
Volume | 138 |
Issue number | 4 |
DOIs | |
Publication status | Published - 2010 Apr |
Keywords
- Dirichlet form
- Scattering length
- Symmetric Markov process
- Time change
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics