This chapter focuses on nonlinear problems related to Thomas–Fermi equation. The expression for Thomas–Fermi functional, e(ρ), is given in the chapter. The problem related to this function, occurring in quantum mechanics is discussed in the chapter. The function ρ to be determined represents a density of electrons. The system consists of electrons and of k positive nuclei of charge mi placed at points ai in space. The functional e has three terms, corresponding respectively to the kinetic energy, the attractive potential energy, and the repulsive potential energy. Even though problem discussed in the chapter are a simple convex minimization problem, it need not have a solution.
All Science Journal Classification (ASJC) codes