On the existence of hydrogen atoms in higher dimensional Euclidean spaces

The question of whether hydrogen atoms can exist or not in spaces with a number of dimensions (D) greater than 3 is revisited. The lowest quantum mechanical stable states and the corresponding wave functions are determined by applying Numerovʼs method to solve Schrödingerʼs equation. States for different angular momentum quantum number and dimensionality are considered. One is lead to the result that hydrogen atoms in higher dimensions could actually exist. The most probable distance between the electron and the nucleus are then computed as a function of D showing the possibility of tiny confined states.

► We argued that the question on the existence of hydrogen atom in spaces with high dimensions is still open. ► We solved numerically the Schrodinger equation for the proper generalized Coulomb equation. ► We showed that there exist stable hydrogen atom states for D>3D>3.