Determining functional derivatives Functional derivative
1 determining functional derivatives 1.1 formula 1.2 examples 1.2.1 thomas–fermi kinetic energy functional 1.2.2 coulomb potential energy functional 1.2.3 weizsäcker kinetic energy functional 1.2.4 entropy 1.2.5 exponential 1.2.6 functional derivative of function 1.2.7 functional derivative of iterated function determining functional derivatives we give formula determine functional derivatives common class of functionals can written integral of function , derivatives. generalization of euler–lagrange equation: indeed, functional derivative introduced in physics within derivation of lagrange equation of second kind principle of least action in lagrangian mechanics (18th century). first 3 examples below taken density functional theory (20th century), fourth statistical mechanics (19th century). formula given functional f [ ρ ] = ∫ f ( r , ρ ( ...