Abstract: The energy levels and the wave functions of two higher excited states （n = 4and 5） for the hydrogen atom in a non-uniform electric field are investigated by using the Mathematica. The level splitting is computed. The three-dimensional image of the electron probability angle distribution for the hydrogen atom in a non-uniform electric field is plotted.

Key words: hydrogen atom, energy level degeneracy, non-uniform electric field, perturbation theory, angle distribution