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.
ASJC Scopus subject areas
- 数学 (全般)