F7122 Introduction to Quantum Mechanics of Molecules and Solids

Faculty of Science
Spring 2009
Extent and Intensity
2/1/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Mgr. Dominik Munzar, Dr. (lecturer)
prof. Mgr. Dominik Munzar, Dr. (seminar tutor)
Guaranteed by
prof. RNDr. Josef Humlíček, CSc.
Department of Condensed Matter Physics – Physics Section – Faculty of Science
Contact Person: prof. Mgr. Dominik Munzar, Dr.
Timetable
Thu 10:00–12:50 Fs1 6/1017
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is a continuation of the courses F5030 (Quantum mechanics) and F6121 (Solid state physics). Quantum theory provides a fascinating picture of the behavior of particles. In addition, however, it allows one to understand why and how the electrons and the nuclei form atoms, and why and how atoms form molecules and extended systems (solids, liquids, clusters). Knowledge of the atomic composition and the geometrical structure then allows one to understand various properties of extended systems. This is not merely an understanding ``in principle'' but an understanding that allows to obtain the structure of extended systems and subsequently many properties of these systems at the qualitative and semiquantitative level (using physically transparent and mathematically relatively simple approaches) or with a fairly high precision (using sophisticated ,,ab-initio'' methods, where the only input parameters are the numbers of electrons, protons, and neutrons). At the end of the course, students should be able to understand the main concepts of this field of physics such as the mean field, the exchange and correlation effects, the covalent bond etc. and solve simple related problems. Both physically transparent and simple models and some elements of rigorous quantum mechanical theory of many-electron atoms will be presented. Illustrative examples from the world of atoms, molecules, traditional solid state materials, and modern materials, that are currently under intense research, will also be given.
Syllabus
  • I. Atoms. 1. Hydrogen atom: summary of the quantum mechanical description and relativistic corrections. 2. Helium atom and the concept of electron correlation. 3. Many-electron atoms. (a) Heuristic approach: Hartree equation and screening of the interaction between the nucleus and the electrons. (b) Rigorous approach using symmetry arguments and the variation principle. 4. Periodic table: explanation of the main trends. II. Molecules. 1. Elements of the theory of molecules: the adiabatic approximation, the Hellman-Feynman theorem and the virial theorem. 2. Quantum-mechanical description of the simplest molecules and the nature of the covalent bond. III. Extended systems. Two starting points. 1. Extended system as a giant molecule. 2. Extended system as a Fermi see of electrons on the background of the nuclei, justification and generalization of the Sommerfeld model. 3. Qualitative aspects of the Coulomb interaction in many-electron systems. 4. Qualitative explanation of the crystal structure of elements and of selected simple compounds. IV. Basic ideas of the modern ab-initio methods, in particular the density-functional theory.
Literature
  • PILAR, Frank L. Elementary quantum chemistry. 2nd ed. Mineola, N.Y.: Dover Publications, 2001, xvi, 599. ISBN 0486414647. info
  • LEVINE, Ira N. Quantum chemistry. 5th ed. Upper Saddle River: Prentice Hall, 1999, x, 739. ISBN 0136855121. info
  • KITTEL, Charles. Úvod do fyziky pevných látek. 1. vyd. Praha: Academia, 1985, 598 s. URL info
  • ASHCROFT, Neil W. and N. David MERMIN. Solid state physics. South Melbourne: Brooks/Cole, 1976, xxi, 826 s. ISBN 0-03-083993-9. info
Assessment methods
Lectures and class exercises, where solutions of typical problems are presented and discussed. The examination consists of a written part (test) and an oral part. Active presence at the class exercises, including solution of a certain amount of problems by the students, is required.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.
  • Enrolment Statistics (Spring 2009, recent)
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