Fundamentals of many-electron System: Hartree-Fock Theory

The basic Hamiltonian in a solid: electronic and ionic parts, the adiabatic approximation;

Single-particle approximation of the many-electron system; single product and determinantal wave functions, Occupation number representation; matrix elements of one and two-particle operators; The Hartree-Fock (H-F) method; the one electron H-F equation; exchange interaction and Fermi hole; Coulomb correlation; the H-F ground state energy.

 

The interacting free-electron gas: Quasi electrons and Plasmons

The interacting electron gas; The coulomb interaction; The Hartree-Fock approximation for the electron gas; Exchange Hole; Screeming, Plasmons; Quasi-electrons; The dielectric constant of the electron gas

 

Spin-spin interaction: Magnons      

Absence of magnetism in classical statistics; Origin of the exchange interaction; Direct exchange, super exchange, indirect exchange and itinerant exchange; Spin-waves in ferromagnets-magnons, spontaneous magnetization, thermodynamics of magnons; Spinwaves in lattices with a basis-ferri- and antiferromagnetism; Measurement of magnon spectrum; Ordered magnetism of valence and conduction electrons, Stoner’s criterion for metallic ferromagnet

 

Density Functional Theory      

Basics of DFT, Comparison with conventional wave function approach, Hohenberg-Kohn Theorem; Kohn-Sham Equation; Thomas-Fermi approximation and beyond: LDA and GGA; Application of DFT in a many body calculation and its reliability.

 

Experimental techniques   

Basic ideas of the techniques of field emission, scanning tunneling and atomic force microscopy, scanning electron microscopy, transmission electron microscopy, X-ray diffraction line broadening, small angle X-ray scattering and small angle neutron scattering; Ultraviolet–visible spectroscopy 

 

 

 

 

 

 

BOOKS RECOMMENDED:

• Stanly Raimes: Many Electron Theory; North Holland Publishing company Amsterdam-London
• O. Madelung: Introduction to Solid State Theory; Springer
• D.Pines and P. Nozier: The Theory of Quantum Liquids; Perseus Books Publishing LLC
• W.A. Harison : Pseudopotentials in the Theory of Metals, Benjamin
• Norman Henry March [2], ‎W. H. Young [3], ‎S. Sampanthar [4]- Many Body Problem; cambridge university press
• P.I. Taylor, A Quantum Approach to the Solid State, Prentice Hall.
• Ech. Steinhardt and Ostulond: Physics of quasi crystals.
• Neil W. Aschoft & N. David Mermin : Solid State Physics, Harcourt Publishers (1976)
• Gerald Burns: Solid State Physics, Academic Press (1985).
• Wlater A. Harrison: Solid State Physics, Dover Publication (1980).
• Harald Ibach and Hans Luth: Solid State Physics: An introduction to Principles of
• Materials Science, Springer (2003).
• F. Seitz and D.Tumbull (Eds.): Solid State Physics, Advances in research and
• applications, supplement 3: A.A. Maraduddin, E.W. Montrol and G.H. Weiss: Theory of
• lattice dynamics in harmonic approximation : Academic Press (1963).
• 13. Callaway: Quantum Theory of Solids Part A & B, Academic Press (1974).
• 14. M.P. Marder: Condensed Matter Physics, Wiley-Interscience (2000).
• H.Ibach and H.Luth: An Introduction of Theory and Experiments- Solid State Physics, Narosa (1991).
• Edo M. Yussouf: Lecture Notes in Physics, No. 283, Electronic band structure and its Applications, Springer – Vertag (1987).
• D.Pines: Elementary Excitations in Solids; Perseus (1999)
• N.H. March and M. Passinello: Collective Effects in Solids and Liquids.
• J.M. Ziman: Principles of the Theory of Solids; Cambridge
• C. Kittel : Quantum Theory of Solids                      
• Richard M. Martin: Electronic Structure- Basic Theory and Practical Methods:
• Cambridge (2004).
• Jorge Kohanoff: Electronic Structure Calculations for Solids and Molecules, Cambridge (2006).
• D.J. Singh & Lars Nordstrom: Plane waves, Psedopotentials and the LAPW method 2^nd Ed. (2006).
• User guide/manual of softwares: WIEN2K,VASP, Quantum Expresso, Abinit
• J.H.Fendler; Nanoparticles and Nanostructured Films: Preparation, Characterization and Application