AMMCS-2013 Semi-Plenary Talk

Variational Principles in Wave-Functional and Density- Functional Formulations of Quantum Mechanics

Mel Levy

Abstract: Variational theorems are important for obtaining approximate solutions to the Schroedinger equation. With this in mind, fundamental variational principles will first be discussed within the wave-functional formulation of quantum mechanics. Then the corresponding variational principles for ground states in density and density-matrix functional theories will be reviewed briefly for the non-degenerate and degenerate situations. Based on these variational principles, properties of the exact functionals will be presented that are difficult to satisfy with approximate functionals. Special emphasis will be given to degeneracies, coordinate scaling, and potentials (functional derivatives). Then, a new time-independent density-functional theory for excited states will be presented for Coulomb systems. The lecture will conclude with a description of certain relevant unsolved mathematical problems, such as one involving an ionization energy convexity property.

Born 1941, in Brooklyn, New York.

Professor Emeritus, Tulane University and North Carolina A&T State University.

Visiting Professor, Duke University (2007-). Professor, North Carolina Agricultural and Technical State University, 2002-2007. Professor, Tulane University, 1976-2002 (presently, Professor Emeritus). Visiting Professor or Visiting Scientist: Oak Ridge National Laboratory; Quantum Theory Project, University of Florida; Instituto Venezolano de Investigaciones Cientificas (I.V.I.C.), Caracas, Venezuela; Institute for Theoretical Physics, University of California at Santa Barbara; Institute of Theoretical Physics, Kossuth Lajos University, Debrecen, Hungary; Department of Physics and Theory Center Cornell University; Lecturer, Department of Chemistry, the University of North Carolina at Chapel Hill, 7/74-7/76.

International Academy of Quantum Molecular Science; International Academy of Mathematical Chemistry; Fellow of The American Physical Society; Editorial Board, Advances in Quantum Chemistry; Advisory Editorial Board, Theoretical Chemistry Accounts; Advisory Editorial Board, Progress in Theoretical Chemistry; Guest Editor: The International Journal of Quantum Chemistry; Tulane Liberal Arts and Sciences, Faculty Research Award, 1998.