Study of hydrogen atom described by a generalized wave equation: what can we still learn about space dimensionality

Francisco Caruso, Vitor Oguri, Felipe Silveira

Published 2020-09-28Version 1

Hydrogen atom is supposed to be described by a generalization of Schr\"odinger equation, in which the Hamiltonian depends on an iterated Laplacian and a Coulomb-like potential $r^{-\beta}$. 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 surprisingly new result is obtained. Indeed, for the first time, we can understand that not only the sign of energy but also the value of the ground state energy of hydrogen atom is related to the threefold nature of space.