Still learning about space dimensionality: From the description of hydrogen atom by a generalized wave equation for dimensions D ≥ 3

Abstract

A hydrogen atom is supposed to be described by a generalization of the Schrödinger equation, in which the Hamiltonian depends on an iterated Laplacian and a Coulomb-like potential r−β. Starting from previously obtained solutions for this equation using the 1/N expansion method, it is shown that new light can be shed on the problem of understanding the dimensionality of the world as proposed by Paul Ehrenfest. A surprising new result is obtained. Indeed, for the first time, we can understand that not only the sign of the energy but also the value of the ground state energy of hydrogen atoms is related to the threefold nature of space.