Abstract
A rigorous iteration method for the solution of nonlinear equations in Banach spaces, due to Isaac Newton and Kantorovic, is reported. We consider its application to three nonlinear problems of atomic and nuclear physics, in finite-dimensional spaces: the ordinary, the constrained and a generalized Hartree-Fock problem. We have proved the existence of a solution of the Hartree-Fock equations and its uniqueness in a definite small region of the functional space, for the nucleus16O. This method converges faster than the usual Hartree algorithm and displays some further advantages.
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