Condensed matter theory lecture notes and problem sets 20142015 dmitri ivanov 1 introduction ref. I recommend the book band theory and electronic properties of solids, by john singleton oxford university press, 2001 as. The theory was originally proposed in 1900 to describe and correlate the electrical and thermal properties of metals. Full text is available as a scanned copy of the original print version. Each wave diffracted by a grating is identified through the component of its wave vector tangential to the grating. Then sommerfelds elementary quantum mechanical theory of metals is discussed. Sommerfeld 1928 applied the principles of quantum mechanics to classical free electron theory. This lecture series constitutes a first undergraduate course in solid state physics delivered in an engaging and entertaining manner by professor steven h. Sommerfeld and the spread of the electron theory of metals article pdf available in historical studies in the physical and biological sciences 172. Sommerfelds free electron theory of metals physics. The lectures are uploaded as pdf files, so you will need adobe acrobat.
It also gives the correct value for the lorentz number. In this chapter the free electron theory of metals as developed by sommerfeld and others will be discussed. Contents 1 the drude and sommerfeld models of metals1. Upperlevel undergraduate course taught at the university of pittsburgh in the fall 2015 semester by sergey frolov. Sommerfeld theory of metals arnold sommerfeld 18681951 ece 407 spring 2009 farhan rana cornell university does not say anything about the electron energy distribution in metals are all electrons moving around with about the same. The model, which is an application of kinetic theory, assumes that the microscopic behaviour of electrons in a solid may be treated classically and looks much like a pinball machine, with a sea of constantly jittering electrons bouncing. According to this theory, the metals containing free electrons obey the laws of classical mechanics. The new and more general bohr sommerfeld theory described the atom in terms of two quantum numbers, while bohr had originally used only one quantum. The development of the quantummechanical electron theory of metals. The classical theory had several conspicuous successes, notably the derivation of the form of ohms law and the relation between the. The theory of woods anomalous diffraction gratings, which was developed some years ago, has been reexamined in order to visualize its physical meaning. Freeelectron model of metals, in solidstate physics, representation of a metallic solid as a container filled with a gas composed of free electrons i. As per his investigation, the behavior of free electron in different possible energy states is explained, how the large number of electrons are disturbed in the energy states.
It was developed in 1927, principally by arnold sommerfeld, who combined the classical drude model. Quantum free electron theory of metals pdf the turn of the twentieth century, of a freeelectron theory of metals and the writing by arnold sommerfeld and. It was developed in 1927, principally by arnold sommerfeld, who combined the classical drude model with quantum mechanical fermidirac statistics and hence it is also known as the drude sommerfeld model. Despite the success with respect to the wiedemannfranz. Get a printable copy pdf file of the complete article 823k, or click on a page image below to browse page by page. Atomic selectrons are delocalised due to overlap of outer orbits. Lecture 4 sommerfeld model, quantum ground state of free electron gas. In 1928, by applying quantum mechanical principles, arnold sommerfeld succeeded in overcoming many of drawbacks of the classical free electron theory, while retaining all the essential features of the classical free electron theory. The course is based on steven simons oxford solid state basics textbook. Handout 2 sommerfeld model for metals free fermion gas in this lecture you will learn.
Dm represents documents in the archives of the deutsches museum in. Ganesh the drude model is inadequate in many respects, e. The development of the quantummechanical electron theory. The drude theory of metals the model kinetic theory of gases. In the bulk of the material, the surface is disregarded altogether and the electrons are completely free. Standard topics such as crystal structure, reciprocal space, free electrons, band theory, phonons, and magnetism are covered. Problems forsolid state physics 3rdyearcourse6 hilary term2011 professor steven h. The new and more general bohrsommerfeld theory described the atom in terms of two quantum numbers, while bohr had originally used only one quantum number. Sommerfeld s extension of the bohr theory in 19151916, it was turned into a powerful tool of atomic research and adopted and further developed by german physicists in particular.
Content fermidirac distribution free electrons, boundary conditions density of levels fermi energy, chemical potential electron speci. Ine here, saw the realization that the new quantum theory could explain, at. This leads to a temperature independent n since the fermi energy for metals is in the 10 4. Sommerfeld theory replaces f b v of drude s theory with f v profound consequences on and c v daniele to oli january 11, 2017 5 48. The drude and sommerfeld models of metals this series of lecture notes covers all the material that i will present via transparencies during this part of the c3 major option. Drude theory of transport in metals a assume a scattering time. The free electron model considers that metals are composed of a quantum electron gas where ions. His theory also predicts a linear dependence of the specific heat for metals at low temperatures.
Get a printable copy pdf file of the complete article 823k, or click on a page image below. However, thoughout the course the material that i write on the blackboard will not necessarily be covered in this transcript. Problems forsolid state physics 3rdyearcourse6 hilary. Groundstate properties of the electron gas 1 groundstate properties of the electron gas 2 the fermidirac distribution 3 thermal properties of the free electron gas 4 the sommerfeld theory of conduction in metals daniele to oli january 11, 2017 3 48. The free electrons, considered identical to the outermost, or valence. Sommerfeld theory of metals in 1928 arnold sommerfeld. Sommerfeld theory of metals a quantum theory of independent free electrons physical picture. Phys560notes2 sommerfeld theory of metals a quantum. Osa the theory of anomalous diffraction gratings and of. Drudes theory treated the electrons as an ordinary classical gas. But according to quantum theory, the free electrons occupy different energy levels, up to fermi level at 0 k. Handout 2 sommerfeld model for metals free fermion gas.
Sommerfeld theory of metals in 1928, arnold sommerfeld discovered that free electrons in metals follow fd statistics. According to this theory, the free electrons obey quantum laws. The weaknesses of the bohr model could be partially eliminated by the physicist arnold sommerfeld. Conduction current in metals em wave propagation in metals skin depth plasma frequency. Free electron theory of metals request pdf researchgate. With the introduction of these subshells, it was finally possible to explain the distribution of the electrons within.
Given its simplicity, it is surprisingly successful in. This series of lecture notes covers all the material that i will present via transparencies during this part of the c3 major option. The valence electrons of the constituent atoms become conduction electrons and move about freely through the volume of the metal. Chapter 6 free electron fermi gas national tsing hua. The simplest metals are the alkali metals lithium, sodium, potassium, na, cesium, and rubidium. The salient features of quantum free electron theory sommerfeld proposed this theory in 1928 retaining the concept of free electrons moving in a uniform potential within the metal as in the classical theory, but treated the electrons as obeying the laws of quantum mechanics. Effect of impurity and temperature on electrical resistivity of metals. However, thoughout the course the material that i write on the.
Sommerfeld theory of metals arnold sommerfeld 18681951 ece 407 spring 2009 farhan rana cornell university does not say anything about the electron energy distribution in metals are all electrons moving around with about the same energy. According to classical theory, the free electrons in a metal have random motions with equal probability in all directions. Sommerfeld himself was nominated 81 times more than any other person but was never awarded the nobel prize. Ueep2024 solid state physics topic 3 free electron in metals 2. When we recall the fact sommerfeld has recently expressed. This in turn will affect the way the electron gas can absorb energy from an external source. The drude model of electrical conduction was proposed in 1900 by paul drude to explain the transport properties of electrons in materials especially metals. Then sommerfeld s elementary quantum mechanical theory of metals is discussed. Based on the debroglie wave concept, he assumed that a moving electron.
I recommend the book band theory and electronic properties of solids, by john singleton oxford. Many of these errors occur because the electrons velocity and energy are deduced from a classical distribution. All metals share common properties excellent electrical conductors excellent thermal conductors shiny when polished all due to the free electrons of the metallic bond outline classical drude theory of metals successes and limitations of the classical model sommerfeld theory of metals. Thz pulses are optoelectronically generated and launched onto 0. The electrons, however, are treated using quantum mechanics.
We report an experimental and theoretical study of thz sommerfeld wave propagation on a single copper wire. Introduction to the electron theory of metals the electron theory of metals describes how electrons are responsible for the bonding of metals and subsequent physical, chemical and transport properties. The treatment of a metal as containing a gas of electrons completely free to move within it. In solidstate physics, the free electron model is a simple model for the behaviour of charge carriers in a metallic solid. The pauli exclusion principle strongly modifies classical maxwellboltzmann expressions for electronic specific heat and electron velocities.
This textbook gives a complete account of electron theory in both periodic and nonperiodic metallic systems. Sommerfeld s free electron theory of metals home sommerfeld s free electron theory of metals in 1928, by applying quantum mechanical principles, arnold sommerfeld succeeded in overcoming many of drawbacks of the classical free electron theory, while retaining all the essential features of the classical free electron theory. Arnold johannes wilhelm sommerfeld, formemrs german. View notes phys560notes2 from phys 560 at university of illinois, urbana champaign. Sommerfeld theory of metals a explain what is meant by the fermi energy, fermi temperature and the fermi. Pdf understanding of physics on electrical resistivity in metals.1090 636 1164 1533 934 1067 924 596 1162 1268 295 1119 1369 701 733 1541 503 551 1147 1234 279 733 489 195 725 112 1378 139 331 619 886 1232 1009 1115 1362 68 640