Questions for exercises from 1998quest98.ps (Postscript file) 22.01.01 Introduction. Walking through the topics, about molecular physics Interesting phenomena Quantum Mechanics, Statistical Physics Structure 24.01.01 Quantum Mechanics Highlights Density - squre modulus of wave function Expectation values in classical probability Quant.Mech. expectation values To every quantity - an operator Hamilton operator H Psi = E Psi Eigenvalues - discrete solutions (sometimes continuous) Commutator Heisenberg (Heisenberg in acoustics) (Born in optics ..... sideremarks) Harmonic Oscillator - Newton Harmonic Oscillator - Quant. Ladder spectrum (equidistant) hbar omega (circular frequency vs. frequency) Sideremarks, illustrations: Rydberg atoms - see later impurity states in semiconducters Crystals as huge molecules Born-Oppenheimer approximation Fix the nuclei, do quant. mech. for electrons Electron energies depend on position of nuclei (for 2 atomic nuclei just the distance) Splitting of levels, origins of bands This might be seen as origin of the bonding The lower level goes down (the united nuclei) 29.01.01 The linear chain of masses on a spring Dispersion relationAshcroft-Mermin chapter 22 pages 430-433Mentioned phase velocity, group velocity (will be done later) relation between omega and k - the 'wave vector' Relation for the density of modes (a note will be prepared) -NOTE Densities (for lattice vibrations; explanation to be added) modedens.gif modedens.m String with two types of atoms (two masses, two branches)Ashcroft-Mermin chapter 22 pages 433-435, see fig. 22.10; two spring constants, not two masses31.01.01 Vibrations of 2-dim and 3-dim lattices Density of modes goes as omega squared Einsteins model for heat capacity (note, picture of the page, jpg 148kB) calculation details, jpg 81kB 05.02.01 Debye's model calculation note, jpg 127kB Table of Debye temperatures table30.jpg, 80kB High resolution, same table table50.jpg 150 kB Origin of the Boltzmann factor NOTEEinstein vs. Debye model: Ashcroft-Mermin page 462. 07.02.01 Elementary transport theory Fourier's law - heat conductivity (deriving expression for kappa in Fourier's law) Group velocity Algebraic Method - harmonic oscillator (for phonons) *NOTE* Eigenmodes (diagonalization of frequencies square...) *NOTE* 12.02.01 Computer (Matlab) Simulations Chains - showing the addition of wave numbers types of vibrations - waves - demonstration Diagonalization of the coupled Harm.Osc. matrix back to phonons mean free path

Umklapp process - see chains above Unharmonic effects: terms of u^3 type Heat conductivity: T-dependence ( T^3 low T, T^(-1) high) Thermal expansion . End of first part 14.02.01 Heat and electrical conductivity of electrons CLASSICAL MODELS a) HEAT CONDUCTIVITY - see phonons b) electrical conductivity Drift velocity from acceleration Conductivity (relation to resistance) Conductivity (sigma) for Cu as an example Wiedemann-Franz law derived Lorenz number CLASSICAL ASSUMPTIONS: a) the gas heat capacity (related to Boltzmann) b) velocity squared replaced by kT 19.02.01 FERMI GAS MODEL Pauli principle Independent particles-independent probabilities Indistinguishable particles -- new form of probability P(r1,r2)=P(r2,r1) Slater Determinant Available states (density of states in k-space) NOTE (scanned) fermi-density.jpg Fermi momentum, Fermi energy, Fermi temperature Lu: No two leaves are the same (Chinese saying) (just opposite of the Indistinguishable particles) 21.02.01 Fermi gas - at nonzero T Heat capacity etc (1 hour only) Sommerfeld integrals: Fermi GasIn Ashcroft-Mermin: Sommerfeld integrals are pages 45-47FermiSom.ps (postscript file, overview) Scanned: sommer-meth-1.jpg (Sommerfeld's method) sommer-meth-2.jpg sommer-eval.jpg (Evaluation details) 21.02.01 Fermi gas - at nonzero T Heat capacity etc (1 hour only) Wiedemann-Franz law in Fermi-gas version 26.02.01 Bloch theorem 28.02.01 Bloch theorem via Fourier NOTE: Bloch.ps (postscript file) 05.03.01 Fourier, bands weak potential limit periodicity in the k-space 07.03.01 started semiclassical motion (forces) (1 hour only) equation for u-function (see note) 12.03.01 semiclassical motion Selfconsistent method (background information - see textbook) 14.03.01 3-dim crystals electronic bands the shape of bands Notes for the model construction of 3-dim bands 3dim-1.jpg 3dim-2.jpg 3dim-3.jpg 19.03.01 -- no lecture 21.03.01 -- no lecture 26.03.01 Semiconductors Energy Gap: diagram of resistivity, photon excitation Evaluation of number of electrons in bands (textbook) Semiconductor equation (textbook) 28.03.01 Semiconductor equation (textbook) Impurity states (textbook) a) Donors (P in Si) (the 'quasiatoms'; see discussion of Rydberg atoms, sideremark 24.01.01) b) Acceptors (Al in Si) HOLES and ELECTRONS 02.04.01 p-n junction 7 page NOTE The placement of Fermi level in acceptor and donor doped semiconductors. The mechanisms leading to the common position of Ferni level. Diffusion current and drift current. Fick's law for diffusion. Diffusion constant. Mobility. Einstein-Nernst relation 04.04.01 p-n junction 7 page NOTE, continued Model for charge density distribution Model for the depletion zone The rectifying function of p-n junctionQuestions for exercises from 1998quest98.ps (Postscript file) 18.04.01 Metals, Fermi surface, thermoelectricity .... Explaining the fermi surface in 2 dimensions Electron motion in magnetic field Cyclotron Frequency ... add formulae here (new *NOTE* ... missing) add references to Ashcroft-Mermin Metals as poly-micro-crystalline Matthiesens rule for conductivity (temperature dependence) . To be added: typical values of v_F, l, tau (relax. time) to be added: Matth. rule relations ( rho sigma l) (sigma cross section) (sigma conductivity; sigma dep. on tau, tau dep. 1/T) (sigma dep. sigma_0 / ( CONST + T ) . 23.04.01 Hall effect NOTE Hall effect, 2 pages Hall effect in semiconductors, mobility: Not in Ashcroft-Mermin . Magnetic field/Magnetism basics NOTE (background information 4 pages) (Table of systems of units; JACKSON's book) System of units (physics the same, but even concepts different) . 25.04.01 Magnetic properties of materials Diamagnetism and Paramagnetism NOTE 3 pages Diamagnetism-atomic origin Understanding of negative susceptibilityAshcroft-Mermin chapter 31 pages 648-649. 30.04.01 Paramagnetic response The g-factor Thermic effects, evaluation of average spin projection Brillouin function for general J and for J=1/2Ashcroft-Mermin chapter 31 pages 653-656Paramagnetism of metals (picture explains easily)Ashcroft-Mermin chapter 31 pages 661-662(Ash.Mer. too detailed on this point) . 02.05.01 Ferromagnetism NOTE 3 pages The effective spin-spin interaction Mean Field theory (the explanation of permanent magnetization) . 07.05.01 Superconductivity .Ashcroft-Mermin chapter 34.09.05.01 Crystal systems, Crystal Structure Crystal lattices .Ashcroft-Mermin chapter 4, chapter 7; parts onlyDetermination of crystal structuresAshcroft-Mermin chapter 6, parts only. .