Infinitesimally weak coupling, infinitely strong singularity of the scattering potential

Details Infinitesimally weak coupling, infinitely strong singularity of the scattering potential Infinitesimally weak coupling, infinitely strong singularity of the scattering potential

2000-06-30

arxiv.org/abs/math-ph/0006033v1

Physics

Mathematical Physics

12 pages, no figures, plain tex

Scientific paper

In scattering by singular potentials $g^2U(s;r)$, the coupling constant $g^2$ is continuously decreased to zero while the stage $s$ of singularity raised simultaneously beyond all limits by some functional relation $F(g^2;s)=0$. In the extreme situation of this double limit, even the mere existence of a nontrivial physical scattering problem is questionable. By iterating a pair of integral equations, the relevant solution is developed here in terms of wave functions into a pair of convergent series, each of which reduces in the double limit $\{g^2\to 0;s\to\infty\}$ to a single term calculable by quadrature.

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