Numerical solutions of three-dimensional helium like atoms from the linear combination of their analogue one-dimensional wave functions

The solutions of Schrödinger wave equations for the ground state of three-dimensional helium atom and its isoelectronic series were obtained from the linear combination of one-dimensional helium-like wave functions. The result shows that the one-dimensional bases along the axes are good choices which facilitate easy numerical integration. The three-dimensional wave function was constructed from the linear combination of the bases and the result was further refined to converge to the exact value using the iteration technique. The resultant ground state energy for the helium atom is with deviation of from the exact value. The method developed is thus demonstrated to be an effective numerical approach to the many-body problem and could be extended to other atomic and molecular systems.