2 research outputs found
Note 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 greater than 3 is revisited, considering higher
dimensional Euclidean spaces. Previous results which lead to different answers
to this question are briefly reviewed. The scenario where not only the
kinematical term of Schr\"odinger equation is generalized to a D-dimensional
space but also the electric charge conservation law (expressed here by the
Poisson law) should actually remains valid is assumed. In this case, the
potential energy in the Schr\"odinger equation goes like 1/r^{D-2}. The lowest
quantum mechanical bound states and the corresponding wave functions are
determined by applying the Numerov numerical method to solve Schr\"odinger's
eigenvalue equation. States for different angular momentum quantum number (l =
0; 1) and dimensionality (5 \leq D \leq 10) are considered. One is lead to the
result that hydrogen atoms in higher dimensions could actually exist. For the
same range of the dimensionality D, the energy eigenvalues and wave functions
are determined for l = 1. The most probable distance between the electron and
the nucleus are then computed as a function of D showing the possibility of
tiny bound states.Comment: 19 pages, 6 figure