2003/02/28 by M. Bawin, S. A. Coon · 5 citations
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #nucl-th #quant-ph
paper · pdf · doi:10.1103/physreva.67.042712
published as Phys.Rev.A67:042712,2003 · Final corrected version to appear in Physical Review A
arxiv created 2003/04/23 · openalex publication_date 2003/04/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the radial Schr"odinger equation for a particle of mass m in the field of a singular attractive \ensuremathα/r2 potential with 2m\ensuremathα>1/4. This potential is relevant to the fabrication of nanoscale atom optical devices, is said to be the potential describing the dipole-bound anions of polar molecules, and is the effective potential underlying the universal behavior of three-body systems in nuclear physics and atomic physics, including aspects of Bose-Einstein condensates, first described by Efimov. New results in three-body physical systems motivate the present investigation. Using the regularization method of Beane et al., we show that the corresponding ``renormalization-group flow'' equation can be solved analytically. We find that it exhibits a limit cycle behavior and has infinitely many branches. We show that a physical meaning for self-adjoint extensions of the Hamiltonian arises naturally in this framework.