The hydrogen atom in α -dimensional space

The hydrogen atom system can be solved strictly by the eigenvalue equation and get analytical solutions, which is uncommon as a quantum mechanics system. In this study, we obtained wave functions and bound state energies of the hydrogen atom by the Schrödinger equation of the hydrogen atom in the noninteger-dimensional space. And we discussed dimensional behavior in binding energy, angular momentum, and radial density. The dimension α is given by the degree of anisotropy of the actual physical system. The excitons in solids are similar to the hydrogen atoms, except that the mass of their center positive charge is different, so the results obtained in this study were also applicable to excitons in anisotropic solids and hydrogenic impurities, which have application value. (paper)