LFU:online

Institut für Theoretische Physik Institut für Theoretische Physik

Dr. Michael Ruggenthaler Dr. Michael Ruggenthaler

705910

Density Functional Theories

VO 2

4

wöch.

keine Angabe

Englisch

Density-Functional Theory (DFT) is one of the most popular approaches to (numerically) determine the ground-state properties of many-body systems. It finds its application in a variety of fields, e.g., condensed matter theory, quantum chemistry or nuclear physics. Although less well developed, also time-dependent DFT (TDDFT) has become a standard tool, e.g., to calculate optical excitation spectra of large molecules. This lecture will focus almost exclusively on the foundations of those two approaches to the many-body problem of quantum mechanics. Outline: 1. Motivation and Introduction (The quantum many-body problem and an example) 2. Many-Body Quantum Mechanics (Brief review of one-particle quantum mechanics in connection with L^p spaces, self-adjoint operators and Sobolev spaces; (anti)symmetrization of the many-body wave function and second quantization; the one-particle density) 3. Ground-State Density-Functional Theory (Properties of the densities and the energy-functional; Hohenberg-Kohn theorems; functional derivative and the Kohn-Sham construction; the local density approximation) 4. Time-Dependent Density-Functional Theory (Quantum fluid dynamics; Runge-Gross and van Leeuwen theorem; linear response theory) 5. If time permits and dependening on the choice of the students (Approximations like the GGA or orbital functionals; relativistic (TD)DFT; connection to Keldysh Green's function techniques...) Prerequisites: Basic quantum mechanics and basic knowledge about mathematical methods in quantum theory (Lebesgue integration, Hilbert spaces,...) Knowledge in many-body theory or functional analysis (distributions, Hilbert space operators, variational methods) are helpful but not needed. All the necessary aspects will be established. The mathematical details will be motivated (by examples if possible) and formally introduced (usually without any proofs). We will break the "no-proofs rule" only for the basic theorems of (TD)DFT.
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