Isomorphism Transformation Between the Hydrogen Atom and Four-Dimensional Harmonic Oscillator

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Abstract

By means of the SU(1,1) algebra we study the relationships between the coordinates, energy, angular momentum, spherical harmonics, and radial function of a hydrogen atom and those of a four-dimensional harmonic oscillator. The energies and angular momenta of the two quantum systems are found to correspond to one another.

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