Degeneracies in energy levels of quantum systems of variable dimensionality

Abstract

Introduction of variable dimensionality to the Schrödinger equation gives rise to interdimensional degeneracies in the energy levels of one−, two−, and three−electron atoms and molecules. In all cases the degeneracies result from a factorization of the wavefunction into a product of a ’’radial’’ type function times an ’’angular’’ type function. Scaling of the orbital angular momentum quantum number in the one−electron radial equation to obtain ’’excess angular momentum’’ is shown to be equivalent to a variation in dimensionality.