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Abstract.We propose an easy and effenive variant of the realization of the dynamical symmetry of hydrogen-like atoms in five-dimensional space, based on the relationship between the Sehr6dinger equation far the isotropic harmonic oscillator in four-dimensional complex space and the SchrSdinger equation for the one-electron atom in five-dimensional space. By the use of the path integral we also establish the relationship between the Coulomb Green function and the Green function for the isotropic harmonic oscillator in fourdimensional complex space.

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