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Title: Crater property in two-particle bound states: When and why

Abstract

Crater has shown that, for two particles (with masses m{sub 1} and m{sub 2}) in a Coulombic bound state, the charge distribution is equal to the sum of the two charge distributions obtained by taking m{sub 1}{yields}{infinity} and m{sub 2}{yields}{infinity}, respectively, while keeping the same Coulombic potential. We provide a simple scaling criterion to determine whether an arbitrary Hamiltonian possesses this property. In particular, we show that, for a Coulombic system, fine structure corrections preserve this Crater property while two-particle relativistic corrections and/or hyperfine corrections may destroy it. (c) 2000 American Association of Physics Teachers.

Authors:
 [1]
  1. Department of Physics, University of Maryland, College Park, Maryland 20742-4111 (United States)
Publication Date:
OSTI Identifier:
20216355
Resource Type:
Journal Article
Journal Name:
American Journal of Physics
Additional Journal Information:
Journal Volume: 68; Journal Issue: 6; Other Information: PBD: Jun 2000; Journal ID: ISSN 0002-9505
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 74 ATOMIC AND MOLECULAR PHYSICS; SCHROEDINGER EQUATION; COULOMB CORRECTION; COULOMB ENERGY; COULOMB FIELD; BOUND STATE; HAMILTONIANS; PERTURBATION THEORY; RELATIVISTIC RANGE; HYPERFINE STRUCTURE; ELECTRONIC STRUCTURE; EDUCATIONAL TOOLS; QUANTUM MECHANICS; THEORETICAL DATA

Citation Formats

Chow, Chi-Keung. Crater property in two-particle bound states: When and why. United States: N. p., 2000. Web. doi:10.1119/1.19482.
Chow, Chi-Keung. Crater property in two-particle bound states: When and why. United States. doi:10.1119/1.19482.
Chow, Chi-Keung. Thu . "Crater property in two-particle bound states: When and why". United States. doi:10.1119/1.19482.
@article{osti_20216355,
title = {Crater property in two-particle bound states: When and why},
author = {Chow, Chi-Keung},
abstractNote = {Crater has shown that, for two particles (with masses m{sub 1} and m{sub 2}) in a Coulombic bound state, the charge distribution is equal to the sum of the two charge distributions obtained by taking m{sub 1}{yields}{infinity} and m{sub 2}{yields}{infinity}, respectively, while keeping the same Coulombic potential. We provide a simple scaling criterion to determine whether an arbitrary Hamiltonian possesses this property. In particular, we show that, for a Coulombic system, fine structure corrections preserve this Crater property while two-particle relativistic corrections and/or hyperfine corrections may destroy it. (c) 2000 American Association of Physics Teachers.},
doi = {10.1119/1.19482},
journal = {American Journal of Physics},
issn = {0002-9505},
number = 6,
volume = 68,
place = {United States},
year = {2000},
month = {6}
}