A Relation between the Hydrogen Atom and Multidimensional Harmonic Oscillators

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Abstract
A simple connection between the radial Schrödinger equation for the bound states of a hydrogen atom with angular momentum l and that of an isotropic harmonic oscillator of even dimension from 2 to 4l + 4 is noted. The case of highest dimensionality 4l + 4 is shown to lead in a very simple way to the energy levels and degeneracies of the hydrogen atom, once the energy levels of a one‐dimensional harmonic oscillator are known.

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