Integral Equation Approach to Bound State Atomic Systems. Preliminary Studies of Helium and Hydrogen

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Abstract
The Sams‐Kouri method for noniteratively solving integral equations is used to solve the integral form of Schrödinger's equation for He such that the Hartree‐Fock approximation is avoided and the inclusion of nuclear motion is straightforward. An exact formalism is presented which requires the solution to coupled integral equations, and the method for generalizing to many electron atoms is indicated. Calculations are reported for a single integral equation approximation to He which illustrates the essential features of the method. The energy value obtained is approximately 85% of the total binding energy. Calculations for the H atom are given so comparisons with an exactly soluble atomic problem can be made, and the energy values for the ground and first three excited states are in excellent agreement with the exact values. Excited state calculations are found to be no more difficult than those for the ground state.