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The research computed the energy levels and radial wave functions of the Hydrogen Atom. The method used for computation was FEM (finite element method). Using the variational method approach, FEM was applied to the action integral of Schrödinger equation. This lead to the eigenvalue equation in the form of global matrix equation. The results of computation were depended on boundary of the action integral of Schrödinger equation and number of elements. For boundary 0 - 100a0 and 100 elements, they were the realistic and best choice of computation to the closed analytic results. The computation of first five energy levels resulted E1 = -0.99917211 R∞, E2 = -0.24984445 R∞, E3 = -0.11105532 R∞, E4 = -0.06247405 R∞ and E5 = -0.03998598 R∞ where 1 R∞ = 13.6 eV. They had relative error under 0.1% to the analytic results.
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