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Title: Quantum solution for the one-dimensional Coulomb problem

The one-dimensional hydrogen atom has been a much studied system with a wide range of applications. Since the pioneering work of Loudon [R. Loudon, Am. J. Phys. 27, 649 (1959).], a number of different features related to the nature of the eigenfunctions have been found. However, many of the claims made throughout the years in this regard are not correct--such as the existence of only odd eigenstates or of an infinite binding-energy ground state. We explicitly show that the one-dimensional hydrogen atom does not admit a ground state of infinite binding energy and that the one-dimensional Coulomb potential is not its own supersymmetric partner. Furthermore, we argue that at the root of many such false claims lies the omission of a superselection rule that effectively separates the right side from the left side of the singularity of the Coulomb potential.
Authors:
; ;  [1] ;  [2] ;  [2]
  1. Departamento de Fisica, Universidad Autonoma Metropolitana, Unidad Iztapalapa, Apartado Postal 55-534, Iztapalapa CP 09340 D. F. (Mexico)
  2. (Mexico)
Publication Date:
OSTI Identifier:
21550229
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 83; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevA.83.064101; (c) 2011 American Institute of Physics
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 74 ATOMIC AND MOLECULAR PHYSICS; ATOMS; BINDING ENERGY; COULOMB FIELD; EIGENFUNCTIONS; EIGENSTATES; HYDROGEN; MATHEMATICAL SOLUTIONS; ONE-DIMENSIONAL CALCULATIONS; QUANTUM MECHANICS; SINGULARITY; SUPERSELECTION RULES; SUPERSYMMETRY ELECTRIC FIELDS; ELEMENTS; ENERGY; FUNCTIONS; MECHANICS; NONMETALS; SELECTION RULES; SYMMETRY