The singular inverse square potential, limit cycles and self-adjoint extensions

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dc.creatorBawin, M.
dc.creatorCoon, S. A.
dc.date2003-02-28
dc.date2003-04-23
dc.date.accessioned2026-07-07T12:04:20Z
dc.date.available2026-07-07T12:04:20Z
dc.descriptionWe study the radial Schroedinger equation for a particle in the field of a singular inverse square attractive potential. 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.
dc.descriptionFinal corrected version to appear in Physical Review A
dc.identifierhttps://arxiv.org/abs/quant-ph/0302199
dc.identifierhttp://arxiv.org/abs/quant-ph/0302199
dc.identifierPhys.Rev.A67:042712,2003
dc.identifierdoi:10.1103/PhysRevA.67.042712
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/208101
dc.subjectQuantum Physics
dc.subjectNuclear Theory
dc.titleThe singular inverse square potential, limit cycles and self-adjoint extensions
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