Energy Spectra of the Coulomb Perturbed Potential in N-Dimensional Hilbert Space

We deal with the solutions to the radial Schröinger equation for the Coulomb perturbed potential in N-dimensional Hilbert space by using two methods, i.e. the power series technique via a suitable ansatz to the wavefunction and the Virial theorem. Analytic expressions for eigenvalues and normalized eigenfunctions are derived. A recursion relation among series expansion coefficients, a condition for convergence of series and inter-dimensional degeneracies are also investigated. As special cases, the problem is solved in 3 and 4 dimensions with some specific parameter values. The obtained analytical and numerical results are in good agreement with the results of other studies.