Radial Coulomb and Oscillator Systems in Arbitrary Dimensions
arXiv:quant-ph/9602007 · doi:10.1063/1.531504
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.
accepted for publication in J. Math. Phys
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