  We propose a new approach to calculate perturbatively the effects of a
particular deformed Heisenberg algebra on energy spectrum. We use this method
to calculate the harmonic oscillator spectrum and find that corrections are in
agreement with a previous calculation. Then, we apply this approach to obtain
the hydrogen atom spectrum and we find that splittings of degenerate energy
levels appear. Comparison with experimental data yields an interesting upper
bound for the deformation parameter of the Heisenberg algebra.
