Operator newton iterative convergence for time dependent density functional theory

Abstract

In a recent publication, the author has established the existence of a unique weak solution of the initial/boundaryvalue problem for a closed quantum system modeled by time dependent density function theory (TDDFT). We describe a Newton iteration, based upon the technique used to prove (unique) existence for the TDDFT model.We show that successive approximation at the operator level, based upon the evolution operator, is sufficient to obtain a `starting iterate' for Newton's method. We discuss the so-called quadratic convergence associated with Newton's method. In the process, we obtain a Kantorovich type theorem for TDDFT.