Radial Coulomb and Oscillator Systems in Arbitrary Dimensions
Quantum Physics
2009-09-25 v1
Abstract
A mapping is obtained relating analytical radial Coulomb systems in any dimension greater than one to analytical radial oscillators in any dimension. This mapping, involving supersymmetry-based quantum-defect theory, is possible for dimensions unavailable to conventional mappings. Among the special cases is an injection from bound states of the three-dimensional radial Coulomb system into a three-dimensional radial isotropic oscillator where one of the two systems has an analytical quantum defect. The issue of mapping the continuum states is briefly considered.
Cite
@article{arxiv.quant-ph/9602007,
title = {Radial Coulomb and Oscillator Systems in Arbitrary Dimensions},
author = {Alan Kostelecky and Neil Russell},
journal= {arXiv preprint arXiv:quant-ph/9602007},
year = {2009}
}
Comments
accepted for publication in J. Math. Phys