The Lower Bound Estimate Of Müller’s Exchange-correlation Energy

In quantum mechanics, the Müller’s exchange-correlation energy is an approxi-mation of many-body Hamiltonian energy. We estimate the lower bound of Müller’sexchange-correlation functional in non-relativistic case and relativistic case. The targetis to use Müller’s exchange-correlation functional studying on the stability of matter ofmany-body Hamiltonian system. In this thesis, we focus on the relaxed problem, whichmeans that the number of electrons is equal or less than N. We want to use the minimizerof the relaxed problem to get the minimizer of the original problem. The main difcultyis that the exchange term is lack of weak lower semi-continuity. We use a part of thekinetic energy to control this part. But the structure of the operator is changed. So it isnot easy to get the minimizer of original problem. It will be studied in the future.