Electronic structure from equivalent differential equations of Hartree-Fock equations

A strict universal method of calculating the electronic structure of condensed matter from the Hartree-Fock equation is proposed. It is based on a partial differential equation (PDE) strictly equivalent to the Hartree-Fock equation, which is an integral-differential equation of fermion single-body wavefunctions. Although the maximum order of the differential operator in the Hartree-Fock equation is 2, the mathematical property of its integral kernel function can warrant the equation to be strictly equivalent to a 4th-order nonlinear partial differential equation of fermion single-body wavefunctions. This allows the electronic structure calculation to eliminate empirical and random choices of the starting trial wavefunction (which is inevitable for achieving rapid convergence with respect to iterative times, in the iterative method of studying integral-differential equations), and strictly relates the electronic structure to the space boundary conditions of the single-body wavefunction.