Abstract: The finite element method is used to obtain numerical solutions of the Schrödinger equation for the Helium 1s2p-state. The relative errors of approximate energies are 10^-6 for triplet and 10^-4 for singlet which are slightly smaller than J. Shertzer's results for the Helium ground state[9]. The generalized eigenvalue problems obtained by FEM are symmetric for the ground state but unsymmetric for 1s2p-state. It becomes more difficult to solve the problems. Form the graphs of wave functions, it can be seen that it is reasonable to solve the Schrödinger equations in bounded domains.

Key words: finite element method, Hyllerass-Breit's transformation, Schrödinger equation