Higher‐Order Finite Difference Solutions of the Schrödinger Equation for the Helium Atom

Higher‐order finite difference solutions of the Schrödinger equation for the helium atom have been obtained. For the S‐limit equation the ground‐ and first‐excited‐state energy values were found. There was a substantial reduction in the difference error in comparison with the treatment of Winter, Diestler, and McKoy (1968). For the complete (nonrelativistic) Schrödinger equation for He finite difference expressions of error ${\mathrm{O(h}}^6)$ gave the ground‐state energy to five significant figures (− 2.9038 hartree). This problem seems to be near the limit of practical solution by the finite difference method.