dorsal/arxiv
View SchemaThe singular inverse square potential, limit cycles and self-adjoint extensions
| Authors | M. Bawin, S. A. Coon |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0302199 |
| URL | https://arxiv.org/abs/quant-ph/0302199 |
| DOI | 10.1103/PhysRevA.67.042712 |
| Journal | Phys.Rev.A67:042712,2003 |
Abstract
We 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.
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"abstract": "We study the radial Schroedinger equation for a particle in the field of a\nsingular inverse square attractive potential. This potential is relevant to the\nfabrication of nanoscale atom optical devices, is said to be the potential\ndescribing the dipole-bound anions of polar molecules, and is the effective\npotential underlying the universal behavior of three-body systems in nuclear\nphysics and atomic physics, including aspects of Bose-Einstein condensates,\nfirst described by Efimov. New results in three-body physical systems motivate\nthe present investigation. Using the regularization method of Beane et al., we\nshow that the corresponding ``renormalization group flow\u0027\u0027 equation can be\nsolved analytically. We find that it exhibits a limit cycle behavior and has\ninfinitely many branches. We show that a physical meaning for self-adjoint\nextensions of the Hamiltonian arises naturally in this framework.",
"arxiv_id": "quant-ph/0302199",
"authors": [
"M. Bawin",
"S. A. Coon"
],
"categories": [
"quant-ph",
"nucl-th"
],
"doi": "10.1103/PhysRevA.67.042712",
"journal_ref": "Phys.Rev.A67:042712,2003",
"title": "The singular inverse square potential, limit cycles and self-adjoint extensions",
"url": "https://arxiv.org/abs/quant-ph/0302199"
},
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