DENSITY-FUNCTIONAL THEORY AS AN EXAMPLE FOR THE CONSTRUCTION OF STATIONARITY PRINCIPLES

From the very beginning, quantum statistical mechanics can be formulat ed in terms of a thermodynamic potential, which has the electron densi ty as the basic variable. By employing a well-known procedure in quant um statistical mechanics for the construction of stationarity principl es [ T. D. Lee and C.N. Yang, Phys. Rev. 113, 1165, (1959); 117,. 22 ( 1960)], the variational principles of Hohenberg, Kohn [ P. Hohenberg a nd W. Kohn, Phys. Rev. B, 136, 864 (1964)], and Mermin [ N. D. Mermin, Phys. Rev. A 137, 1441 (1965)] are obtained as are generalizations th ereof.