Related papers: Still learning about space dimensionality: from the description of hydrogen atom by a generalized wave equation for dimensions D$\geq$3

Still learning about space dimensionality: from the description of hydrogen atom by a generalized wave equation for dimensions D$\geq$3

URL: http://arxiv.org/abs/2009.13473v2
Date: Mon, 7 Nov 2022 16:49:30 GMT
Title: Still learning about space dimensionality: from the description of hydrogen atom by a generalized wave equation for dimensions D$\geq$3
Authors: Francisco Caruso, Vitor Oguri, Felipe Silveira
Abstract summary: It is shown that new light can be shed on the problem of understanding the dimensionality of the world. 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.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: The hydrogen atom is supposed to be described by a generalization of Schr\"{o}dinger 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.

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