The three-dimensional hydrogen atom as a restricted four-dimensional harmonic oscillator

Abstract

It is shown that the study of the quantum hydrogen-atom problem is equivalent to that of a quantum harmonic-oscillator problem in four dimensions, restricted by a superselection rule which results from the invariance of the physical states under the transformations of a one-parametric subgroup of O(4), the kernel of the transformation used. A projected hamiltonian is built up and a specific perturbational technique is developed. © 1973.