Abstract
The energy spectrum of a nonrelativistic particle in radial potentials of the form V(r) = αr 2d−2 − βr d−2 shows one level with a singularly high multiplicity. The two-dimensional problems are focused upon and the constants of motion that generate the symmetries responsible for this local accidental degeneracy are determined. The conserved operators realize an SU(2) algebra and the bound states are seen to fall into either finite, semibounded, or unbounded representations of this algebra. An SO(3,2) module encompassing the eigenstates associated to the whole set of potentials is also identified. It is further shown that there exists a second coordinate system besides the polar one in which the Schrödinger equation separates. Finally, it is indicated how the two-dimensional Coulomb and harmonic oscillator problems arise as special cases.
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