On hydrogen-like atoms in N-dimensional space

This study provides an analytical solution to the Schrödinger equation for hydrogen-like atoms within the context of N-dimensional Euclidean space. The eigenvalue problem associated with the angular component is solved in a manner akin to the N = 3 scenario, bypassing the need for harmonic analysis. Both graphical and tabular representations are used to illustrate the characteristics of the radial and angular eigenstates, including their degeneracy. We investigate the influence of dimensionality on energy, stability, atomic spectra, and degeneracy. Furthermore, we examine how the choice of potential function impacts the existence of atomic structures.