Abstract: A variational method of two parameters for studing ground state energys and wave functions of the helium atom and quasi-heliumion is proposed. We have designed the tested the wave function and derive the ground level expression by solving the radial Schroedinger equation. The ground energy is evaluated by means of the optimized computation of Mathematica 5.0. Our result is compared with the experimental data and the result of other variational methods. It is shown that our result is much precision and the number of variational parameters is less than that of other methods. Meanwhile the importance of permutation symmetry and entanglement of quantum state in the system of two-electron atom is emphasized.

Key words: variational method, helium atom, ground-state energy, permutation symmetry, entangle state