Finite-difference solution to the Schroedinger equation for the ground state and first-excited state of helium

The Schroedinger equation for S-type states of the helium atom, which is an elliptic partial-differential equation, is converted to a set of finite-difference equations, which are then solved by an iterative technique. The total energy of the ground state and first-excited state are calculated to be -2.90360 and -2.17414 a.u., respectively, as compared to the known accurate values of -2.90372 and -2.17522 a.u. due to Pekeris. The results for the ground state include energy expectation values and expectation values of other terms commonly used to test the correctness of the wave function. Reasonable agreement is obtained between values obtained by this work and that of Pekeris, with the differences being within the known numerical error of the iterative method. 7 tables