2000/06/30 by T. Dolinszky, Dolinszky, T.
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Crystallography and Radiation Phenomena #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Mechanics and Non-Hermitian Physics #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.math-ph/0006033
12 pages, no figures, plain tex
arxiv created 2000/06/30 · openalex publication_date 2000/06/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In scattering by singular potentials g2U(s;r), the coupling constant g2 is continuously decreased to zero while the stage s of singularity raised simultaneously beyond all limits by some functional relation F(g2;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 \g2→ 0;s→∞\ to a single term calculable by quadrature.