Solution of the Schrodinger equation in two and three dimensions

Eigenvalues and eigenfunctions of the Schrodinger equation are computed by a finite-difference method that is very simple and fast. An arbitrary initial solution and an eigenvalue are first assumed. Then, a 'correction' formula is used to improve the accuracy of E and the solution at each point of the domain mesh. The correction formula is obtained by simply substituting in the Schrodinger equation the finite-difference expressions for the derivatives. In two dimensions, the ground state of helium and that of the hydride ion are computed in the S-limit approximation. In three dimensions the computations include the ground state of the unapproximated helium atom (two-electron systems) and that of the lithium atom in the S-limit approximation. The method is thousands of times faster than the matrix method used previously by the author, and is millions of times faster than the other FD methods and the variational methods.