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Topic: Free electron model

	Free electron model - Wikipedia, the free encyclopedia
		In physics, the free electron model is a possible model for the behaviour of electrons in a crystal structure of a metallic solid.
		While this model is the simplest model, it reproduces the main electronic properties of metals.
		the electrons move in a constant energy potential (the structure of the material is completely ignored).
	en.wikipedia.org /wiki/Free_electron (248 words)

	FEL Pendulum Model
		The energy released by the electron increases the laser field and consequently lowers the minimum further.
		The position of the electron is determined by the pondermotive (or electron) phase,
		The pendulum FEL model is valid for both weak or strong optical fields and for high or low gain.
	webphysics.davidson.edu /Applets/FELPart/FelOde.html (679 words)

	JLN Labs - The Newmans's Machine Cooling effect
		Electrons with the highest allowed energy level in a given valence band will be reflected (in a perfect crystal) or at least scattered when they reach a forbidden energy level.
		In this way electrons in valence bands simply exchange energy levels such that there is not net gain in energy (speed) in a single direction and therefore no net current flow due to the electrons in the valence bands.
		The electron at level 1 however is not allowed to go to a lower level in the reverse direction and is reflected so that it would now occupy level 1 of the forward direction.
	jnaudin.free.fr /html/NewMcool.htm (2086 words)

	Energy bands (Site not responding. Last check: 2007-10-17)
		This model assumes that electrons are free to move within the metal but are confined to the metal by potential barriers as illustrated by Figure 2.3.1.
		The core electrons are tightly bound to the atom and are not allowed to freely move in the material.
		The electrons in the almost-empty band are negatively charged particles, which therefore move in a direction, which opposes the direction of the field.
	ece-www.colorado.edu /~bart/book/book/chapter2/ch2_3.htm (3344 words)

	free-electron model of metals -- Encyclopædia Britannica (Site not responding. Last check: 2007-10-17)
		in solid-state physics, representation of a metallic solid as a container filled with a gas composed of free electrons (i.e., those responsible for high electrical and thermal conductivity) that move in a virtually uniform potential arising largely from metal ions in the crystal lattice.
		The free electrons, considered identical to the valence electrons of free metal...
		A scale model is an exact miniature that, though much smaller than the original, has all the same components in proportion to those of the original.
	www.britannica.com /eb/article-9035281 (787 words)

	Understanding Physics (Michael Mansfield and Colm O' Sullivan)
		The free electron model is introduced quantitatively for metals and then developed qualitatively, through the band model, to apply to insulators and semiconductors.
		In Section 20.2 it is shown that the classical free electron (Drude) model of the microscopic behaviour of electrons in a metal fails to account quantitatively for properties such as electrical conductivity and specific heat capacity.
		In Sections 20.3 to 20.5 the microscopic behaviour of electrons in metals is shown to be governed by quantum mechanical considerations and, in Section 20.6, the quantum free electron model is shown to account for the electrical conductivity and specific heat capacity of metals quantitatively.
	www.ucc.ie /publication/mansfield/books/uphys/book/chap20.htm (653 words)

	Hans Kuhn: Replication to Michael Kasha- Component of : Early Ideas in the History of Quantum Chemistry.
		Later on, Bayliss considered a π-electron as an electron in the sigma-bonded lattice intending to give a refinement of the free electron model.
		In contrast, I considered the free electron model as a clever way to take account of the interaction between π- electrons: a given π-electron is in the field of the closest positively charged C-atom, the charges on all other C-atoms in the chain is shielded by the other π-electrons.
		The free electron model (in this refinement and by taking into account the correlation of π-electrons in the field of an incident light wave) is much more usefu1 in treating problems of present day’s interest than generally assumed (see e.g.
	www.quantum-chemistry-history.com /Kuhn_Dat/Kuhnx_replic/Kuhnx_replica.htm (924 words)

	Free Electron Lasers
		Free Electron Lasers (FELs) are unlike conventional lasers.
		There are a variety of ways of achieving this - by using magnetic fields or simply passing the electron beam near the surface of a material.
		This is between "Elements of Quantum Optics" and "Lectures on the Free Electron Laser..." in difficulty.
	homepages.nildram.co.uk /~phekda/richdawe/fel (327 words)

	Stefan Birner: Density of states (Essay)
		The motion of the electrons is in the
		One of the failures of the free electron theory was that the heat capacity of the electrons was
		Einstein model of the density of states to derive the heat capacity (used to approximate the optical phonon part of the phonon spectrum)
	www.asamnet.de /~birners/public_html/density.html (953 words)

	Bayliss, Noel Stanley 1906-1996 - Component of : Early Ideas in the History of Quantum Chemistry.
		It was already widely known that the -electrons could move freely along the system of conjugated double bonds, and the theoretical energy levels of an electron oscillating in a box with a vertical potential profile at each end had already been analysed.
		The free-electron model caused a brief flurry of attention; it was attractive in its simplicity and it emphasized the mobility of the -electrons in a conjugated chain.
		However, by the early 'fifties it was clear that the future of that kind of work lay with the electronic computers that were beginning to be available in a few major centres, but certainly not in Western Australia, and he discontinued free-electron calculations in favour of other interests.
	www.quantum-chemistry-history.com /Bayliss1.htm (1033 words)

	[No title]
		Hall effect E. Thermal conductivity of metals F. Nearly free electron model and the energy gap G. Block functions H. KronigPenny model I. Wave equation of electron in a periodic potential 1.
		Kinetic Energy of Electron Gas Show that the kinetic energy of a threedimensional gas of N electrons at 0K is: UO = (3/5)N(F, where (F is the Fermi energy.
		Note: the density of orbitals of a free electron gas in two dimensions is independent of energy: D(() = L²m/((2, per unit area of specimen.
	www.cbu.edu /~jholmes/P353/PART3.DOC (1340 words)

	McGraw-Hill AccessScience: Free-electron theory of metals (Site not responding. Last check: 2007-10-17)
		The theory was originally proposed in 1900 to describe and correlate the electrical and thermal properties of metals.
		Later, quantum mechanics became the basis for the theory of most of the general properties of simple metals such as sodium, with one free electron per atom, magnesium with two, and aluminum with three.
		Transition metals, such as iron, have partially filled electronic d states and are not treated by the free-electron model.
	www.accessscience.com /Encyclopedia/2/27/Est_271210_frameset.html (143 words)

	[No title]
		To introduce some of the most important properties of the solid state, showing how the electrical, mechanical and thermal properties of crystalline solids may be related to the arrangements of the atoms and the behaviour of electrons within them.
		Free electron hypothesis, Fermi sea, 1-D metal, running wave boundary conditions, reciprocal space representation, 3-D metal, Fermi wavevector and energy, density of states, thermal energy of Fermi sea, electronic specific heat, spin susceptibility, relation to ferromagnetism.
		Equation of motion for electrons in a periodic potential, crystal momentum, effective mass, motion in a constant magnetic field, electrons, vacancies and holes.
	www.physics.gla.ac.uk /Physics4/cg/soli.html (789 words)

	Electrons in metals (from thermodynamics) -- Britannica Student Encyclopedia
		Many of the electronic properties of metals can be understood in terms of a free-electron model, where the valence electrons are treated as an ideal Fermi-Dirac gas.
		Although the valence electrons in a metal interact with each other and with the atomic cores through an electric potential, this r
		Chemical bonds are the transfer, or sharing, of electrons between atoms.
	www.britannica.com /ebi/article-52901 (767 words)

	No Title (Site not responding. Last check: 2007-10-17)
		Where of course this is a great simplification, and should be an upper bound for the nearly-free electron model.
		Ultimately, the conductivity (which is the reciprocal of the resistivity) should roughly be proportional to the number of excited electrons able to carry the current.
		The ratio of the fraction of free electrons for the conductor to the insulator is roughly
	www.pha.jhu.edu /~c171_202/hw9/hw9.html (867 words)

	PHYS 437 / METM 305 Home Page (Site not responding. Last check: 2007-10-17)
		Lattice vibrations: elastic waves, enumeration of modes, Debye and Einstein models, phonons, density of states of a lattice, theory of specific heat, thermal conductivity, scattering by phonons lattice optical properties in the infrared.
		Free-electron model: conduction electron, free-electron gas, electrical conductivity and resistivity, Fermi surface, thermal conductivity in metals, motion in a magnetic field, optical properties, failure of the free-electron model.
		Dielectric and optical properties: dielectric constant and polarizibility, dipolar, ionic and electronic polarizibility, piezoelectricity and ferroelectricity.
	www.iit.edu /~segre/phys437 (251 words)

	2.1.1 Essentials of the Free Electron Gas
		The free electron gas model is a paradigm for the behavior of electrons in a crystal, you should be
		For potential energies, there is always a free choice of zero potential; here it is convenient to put the bottom of the potential well at zero potential energy (we will change that later).
		In this case the probability that a given energy state is occupied by more than 1 electron is negligible, and the exclusion principle is not important because there are always plenty of free states around- the electrons behave akin to classical particles.
	www.tf.uni-kiel.de /matwis/amat/semi_en/kap_2/backbone/r2_1_1.html (1339 words)

	Jaffé, Hans. H. - Component of : Early Ideas in the History of Quantum Chemistry.
		His major interest has been with the mathematical description of the electron density in organic molecules and how this electron distribution affects the properties of such molecules; in short, molecular orbital theory.
		"The Use of Free Electron Model Wave Functions in the Derivation and Representation of LCAO (Molecular Orbital) Wave Functions of Conjugated Molecules", Journal of Chemical Physics, 21, 1287-92 (1953).
		"All-Valence Electron Calculations of the Electronic Spectra of Heterocyclic Molecules" in Quantum Aspects of Heterocyclic Compounds in Chemistry and Biochemistry; The Jerusalem Symposium on Quantum Chemistry and Biochemistry, II, The Israel Academy of Sciences and Humanities, Jerusalem, 1970, pp.
	www.quantum-chemistry-history.com /Jaffe1.htm (5243 words)

	Introduction to the Physics of Electrons in Solids - Cambridge University Press (Site not responding. Last check: 2007-10-17)
		This book aims to introduce the reader to the behaviour of electrons in solids, starting with the simplest possible model, and introducing higher-level models only when the simple model is inadequate.
		Unlike other solid state physics texts, this book does not begin with complex crystallography, but instead builds up from the simplest possible model of a free electron in a box.
		The approach is to introduce the subject through its historical development, and to show how quantum mechanics is necessary for an understanding of the properties of electrons in solids.
	www.cambridge.org /catalogue/print.asp?isbn=0521283582&print=y (198 words)

	To all academic staff
		Learning outcomes: Students should: understand what approximations need to be applied to allow the single-particle Schrodinger equation to describe macroscopic scale systems; the basic formulation of standard models such as the nearly-free electron model and the tight binding model; understand how macroscopic observables derive from fundamental properties; insight into the future development of advanced materials.
		Free Electron Fermi Gas: Free electron energy bands, Fermi energy, Fermi surface, density of states, Finite temperatures, Fermi junction, DC electrical conductivity, Magnetic susceptibility of the electron gas, Magnetic ordering in the interacting electron gas.
		Nearly Free Electron Model, Origin of energy bands, Magnitude of the energy gap, Fourier expansion of periodic properties, Reciprocal lattice, Brillouin zones, Bloch’s theorem, Nearly free electron theory, Constant energy surfaces, Density of states function.
	www.le.ac.uk /physics/teach/recruit/year3/opt4311.htm (235 words)

	PHY389 F2000 Lecture 14 (Site not responding. Last check: 2007-10-17)
		Chose non-interacting electron gas as the simplest model for electrons
		The first step: the NEARLY free electron model in one dimension
		Consider the lattice as a weak effect upon the free electron gas that we studied before
	www.physics.uiuc.edu /research/electronicstructure/389/lnotes/389-lect14.html (188 words)

	Physics 518 Lectures, Spring 2002
		Resistive and Reactive response of the electron gas.
		Compact formulation of density of states for degenerate electron gas.
		Comparison of phonon and electronic contribution to specific heat.
	dept.physics.upenn.edu /~mele/archives/webpage518/phys518.s02/log.html (725 words)

	Galactic Free Electron Density Model---NE2001
		This document provides an interface to the Cordes-Lazio model for the Galactic distribution of free electrons (Cordes and Lazio 2002).
		Cordes, J. and Lazio, T. A New Model for the Galactic Distribution of Free Electrons and its Fluctuations";
		Using Radio Propagation Data to Construct a Model for the Galactic Distribution of Free Electrons"; astro-ph/0301598
	rsd-www.nrl.navy.mil /7213/lazio/ne_model (338 words)

	p263-tst1.f95 (Site not responding. Last check: 2007-10-17)
		There is a unique definition of the effective mass of an electron in a particular partially-filled band.
		In the BCS model of a superconductor, suppose the Debye frequency were doubled.
		Consider an electron orbiting about a magnetic field H in the z direction.
	www.physics.umd.edu /courses/Phys731/einstein/tsts/fe98.htm (834 words)

	ELEG 621 Solid State Electronics II
		for the free electron model (for kT << E
		(the reference energy at top of band for an electron that is free or outside of the solid) with respect to the zero of energy (bottom of occupied band) in the free electron model of Na is 5.0 eV, calculate the maximum wavelength for photoemission (i.e.
		If the vacuum level in a metal with atomic weight 60 lies 6 eV above the zero energy (bottom of band) of the free electron distribution, what must the density of a metal be, in which each atom contributes one free electron, if the photon threshold for photoemission is 2 eV?
	www.eecis.udel.edu /~kolodzey/courses/ELEG621F03/621HmwkFall03/621hw4.htm (340 words)

	[No title]
		It can be shown that electrons are bound, but that the average potential is quite smooth.
		One of the key elements in the success of the nuclear shell model is the long nucleon mean path in nuclear matter.
		It would be nice if the validity of the nuclear shell model were understood as well as, say, the validity of the free-electron model of metals.
	www.physics.ucla.edu /~moszkows/np30/ipmliq~1.htm (643 words)

	[No title] (Site not responding. Last check: 2007-10-17)
		A simpler model of the electronic structure of a metal is called the “free electron model.” According to the free electron model, the potential energy of bonding electrons inside a metal consists of only one term, i.e., a constant potential energy.
		That is, the free electron model differs from our model of a metal because the free electron model does not include “the potential energy of an electron in the electrostatic field of a positively charged ion core.” Explain why the name “free electron” model is very appropriate.
		(Hint: According to the free electron model, what is the magnitude of the forces acting on bonding electrons?) Sketch the probability amplitudes of the lowest energy state of the bonding electrons in a metal that consists of a chain of six atoms according to (1) the free electron model, and (2) our model.
	www.mse.berkeley.edu /Classes/e45/hw/E45_PS5.doc (1109 words)

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