Abstract
The Schrödinger equation in higher dimensions is considered. It consists of the kinetic energy part given by the corresponding Laplace operator, and a term describing the interaction with the electrostatic field of a point charge. From Rutherford-type scattering experiments one can conclude that the potential of a point charge is ∼1/r irrespective of the dimension of the space where the experiment is carried through. Also the structure of the kinetic energy is unchanged in higher dimensions so that one is lead to the result that there exist stable atoms in higher spatial dimensions d⩾4. The solutions and energy eigenvalues to this Schrödinger equation in higher dimensions are presented. As a consequence, the dimensionality of space can be read off from the spectral scheme of atoms: The three-dimensionality of space is a consequence of the existence of the Lyman series. Another consequence is that the Maxwell equations in higher dimensions must be modified in order to have the 1/r-potential as solution for a point charge.
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