Fermi-Dirac statistics

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	Fermi-Dirac statistics - Wikipedia, the free encyclopedia
		F-D statistics was introduced in 1926 by Enrico Fermi and Paul Dirac and applied in 1927 by Arnold Sommerfeld to electrons in metals.
		Fermi-Dirac statistics apply to fermions (particles that obey the Pauli exclusion principle), Bose-Einstein statistics apply to bosons.
		Maxwell-Boltzmann statistics are particularly useful for studying gases F-D statistics are most often used for the study of electrons in solids.
	en.wikipedia.org /wiki/Fermi-Dirac_statistics (1346 words)

	Gas in a box - Wikipedia, the free encyclopedia
		Using the results from either Maxwell-Boltzmann statistics, Bose-Einstein statistics or Fermi-Dirac statistics we use the Thomas-Fermi approximation and go to the limit of a very large box, and express the degeneracy of the energy states as a differential, and summations over states as integrals.
		This simple model can be used to describe the classical ideal gas as well as the various quantum ideal gases such as the ideal massive Fermi gas, the ideal massive Bose gas as well as black body radiation which may be treated as a massless Bose gas.
		In the derivation of Bose-Einstein statistics, when the restraint on the number of particles is removed, this is effectively the same as setting the chemical potential(μ) to zero.
	en.wikipedia.org /wiki/Gas_in_a_box (1289 words)

	AllRefer.com - statistical mechanics (Physics) - Encyclopedia
		In its modern form, statistical mechanics recognizes three broad types of systems: those that obey Maxwell-Boltzmann statistics, those that obey Bose-Einstein statistics, and those that obey Fermi-Dirac statistics.
		Maxwell-Boltzmann statistics apply to systems of classical particles, such as the atmosphere, in which considerations from the quantum theory are small enough that they may be ignored.
		Photons, for instance, are bosons, and so the study of electromagnetic radiation, such as the radiation of a black body involves the use of Bose-Einstein statistics.
	reference.allrefer.com /encyclopedia/S/statmech.html (463 words)

	Search Results for "Statistics"
		statistics, science of collecting and classifying a group of facts according to their relative number and determining certain values that represent characteristics...
		Statistics concerning the important events in human life, such as births, deaths, marriages, and migrations....
		...vital statistics, primarily records of the number of births and deaths in a population.
	www.bartleby.com /cgi-bin/texis/webinator/sitesearch?FILTER=&query=Statistics (314 words)

	Fermi level and Fermi function
		The Fermi function comes from Fermi-Dirac statistics and has the form
		The Fermi function gives the probability of occupying an available energy state, but this must be factored by the number of available energy states to determine how many electrons would reach the conduction band.This density of states is the electron density of states, but there are differences in its implications for conductors and semiconductors.
		The concept of the Fermi energy is a crucially important concept for the understanding of the electrical and thermal properties of solids.
	hyperphysics.phy-astr.gsu.edu /hbase/solids/fermi.html (934 words)

	Nobel laureate Cronin edits book on Fermi’s legacy
		In the 1920s, he built on quantum theory by formulating concepts called Fermi energy and, with Paul Dirac, Fermi-Dirac statistics.
		Fermi went on to earn the Nobel Prize in 1938 for his discovery of new radioactive elements produced by the addition of neutrons to the cores of other atoms, and for the discovery of nuclear reactions brought about by slowly moving neutrons.
		Among Fermi’s early accomplishments was to apply quantum mechanics, which explains the behavior of atoms and subatomic particles, to the physics of solids and gases, Cronin said.
	chronicle.uchicago.edu /041007/fermi.shtml (750 words)

	AllRefer.com - elementary particles : Classification of Elementary Particles (Physics) - Encyclopedia
		Fermi-Dirac statistics apply to those particles restricted by the Pauli exclusion principle; particles obeying the Fermi-Dirac statistics are known as fermions.
		Two types of statistics are used to describe elementary particles, and the particles are classified on the basis of which statistics they obey.
		Bose-Einstein statistics apply to all particles not covered by the exclusion principle, and such particles are known as bosons.
	reference.allrefer.com /encyclopedia/E/elementr-p-classification-of-elementary-particles.html (374 words)

	ScienceWeek
		Quantum statistics, in turn, takes one of two forms, depending on distribution constraints: Fermi-Dirac statistics or Bose-Einstein statistics.
		Bose-Einstein statistics is the statistical mechanics of a system of indistinguishable particles for which there is no restriction on the number of particles that may simultaneously exist in the same quantum energy state.
		In general, quantum statistics is concerned with the equilibrium distribution of elementary particles of a particular type among the various possible quantized energy states, with an assumption that these particles are indistinguishable.
	scienceweek.com /2003/sw030404.htm (10906 words)

	Britney Spears Guide to Semiconductor Physics: Fermi-Dirac Statistics
		Britney Spears Guide to Semiconductor Physics: Fermi-Dirac Statistics
		When the Fermi distribution is multipled by the density of states, and integrated over the energy of the band the carrier concentration is results.
		The probability of an energy level being occupied is dependent on the temperature and the Fermi energy.
	britneyspears.ac /physics/fdstats.html (445 words)

	pracfkey.htm
		What is the distinguishing characteristic between particles that obey Bose-Einstein statistics and those that obey Fermi-Dirac statistics?
		For Fermi-Dirac statistics we can put only two particles into the same energy state.
		For Bose-Einstein statistics, there is no limit to the number of particles that may be placed in the lowest energy state.
	www.usd.edu /phys/courses/phys431/exams/pracfkey.htm (442 words)

	Fermi-Dirac Distribution Example
		Fermi-Dirac statistics differ dramatically from the classical Maxwell-Boltzmann statistics in that fermions must obey the Pauli exclusion principle.
		Low energy states are less probable with Fermi-Dirac statistics than with the Maxwell-Boltzmann statistics while mid-range energies are more probable.
		The average for each of the 9 states is shown above compared to the results obtained by Maxwell-Boltzmann statistics and Bose-Einstein statistics.
	hyperphysics.phy-astr.gsu.edu /hbase/quantum/disfdx.html (291 words)

	Spin and Statistics
		Fermions obey Fermi-Dirac statistics, and hence obey the Pauli exclusion principle.
		The spin-statistics theorem of quantum field theory says that particles with half-odd-integer spin (like the electron) must be fermions, while particles with integer spin (like the photon) must be bosons.
		The difference in statistics stems from the properties of the exchange operator.
	math.ucr.edu /home/baez/lie/node16.html (116 words)

	NIST: Methane Symmetry Operations - Nuclear spin stats
		Note that neither Fermi-Dirac nor Bose-Einstein statistics place requirements on the behavior of the complete wave function under the laboratory-fixed inversion operation.
		Bose-Einstein statistics require the complete wave function to be invariant with respect to both kinds of deuteron permutations.
		Table 17 indicates which nuclear spin functions must be combined with rovibrational functions of given symmetry to yield allowed overall wave-functions, and thus illustrates how the well-known [32] statistical weights arise.
	physics.nist.gov /Pubs/Methane/chap092.html (336 words)

	Climbing Humor - Quantum Climbing Mechanics
		Particles of this type are known as Fermions.
		Sport climbers on the other hand follow Bose-Einstein statistics.
		No, any statistical physicist should be able to explain the problem - mountaineers and sport climbers follow different rules.
	www.snowman-jim.org /climbing/humor/stat-mech.html (199 words)

	Fermion
		In Fermi-Dirac and Bose-Einstein statistics "y" is a function of temperature and particle concentration,.
		Fermi-Dirac statistics deals with the energy distribution of fermions.
		The Fermi-Dirac distribution equation which is used to compute the average number of fermions in a particular energy state was developed in 1926 by the physicists Enrico Fermi and P.A.M. Dirac.
	home.earthlink.net /~tdp/fermion.html (224 words)

	Braid statistics -
		In mathematics and theoretical physics, braid statistics is a generalization of the statistics of bosons and fermions based on the concept of braid group.
	psychcentral.com /psypsych/Braid_statistics (91 words)

	PSIgate - Physical Sciences Information Gateway: Search/Browse Results
		The subject is explained in thirteen chapters, including thermodynamics, statistical thermodynamics, evaluation of the partition function and partition functions in particular cases, separate contributions to thermodynamic functions, internal energy and heat capacities, entropy, nuclear spin statistics, chemical equilibrium, rate constants, the Boltzmann distribution and the Fermi-Dirac distribution.
		They cover: an introduction to statistical mechanics; distribution law; indistinguishable particles; statistical mechanics and thermodynamic laws; applications of Maxwell Boltzmann statistics; paramagnetic systems; applications of Fermi Dirac statistics; applications of Bose Einstein statistics; the classical limit; and the kinetic theory of gases.
		These include: thermodynamics, classical statistical mechanics, quantum statistical mechanics, Bose-Einstein statistics, Fermi-Dirac statistics, photon distribution function and thermodynamic equilibrium.
	www.psigate.ac.uk /roads/cgi-bin/psisearch.pl?term1=Fermi-Dirac&subject=All&limit=0 (1718 words)

	Short Biography of frequently mentioned Scientists
		The dirac delta function and the Fermi-Dirac statistics are named after him.
		The Fermi function, the fermi energy, fermions and Fermilab in Chicago are named after him.
		Paul Adrien Maurice Dirac, 1902 - 1984, English physicist known for his pioneering work in the area of quantum-electro-dynamics.
	ece-www.colorado.edu /~bart/ecen5355/newbook/people.htm (455 words)

	Photon statistics
		It follows, from the above discussion, that photons obey a simplified form of Bose-Einstein statistics in which there is an unspecified total number of particles.
		This type of statistics is called photon statistics.
		Thus, for the special case of a gas of photons there is no requirement which limits the total number of particles.
	farside.ph.utexas.edu /teaching/sm1/lectures/node79.html (183 words)

	The Fermi-Dirac Distribution
		At absolute zero, the probability is =1 for energies less than the Fermi energy and zero for energies greater than the Fermi energy.
		The significance of the Fermi energy is most clearly seem by setting T=0.
		We picture all the levels up to the Fermi energy as filled, but no particle has a greater energy.
	hyperphysics.phy-astr.gsu.edu /hbase/quantum/disfd.html (121 words)

	Fermi-Dirac statistics
		quantum statistics defining the possible arrangements of particles in a given system in terms of the exclusion principle.
	www.infoplease.com /dictionary/Fermi-Dirac+statistics (35 words)

	H2G2
		The Fermi-Dirac statistics were calculated independently by the pioneering quantum physicists Enrico Fermi [The element fermium with 100 protons is named after him, as was the Fermilab accelerator in Illinois.
		If a particle is fermionic, it is one that obeys the Fermi-Dirac statistics.
		They are rules that determine the behaviour of a limited number of quantum particles, called fermions.
	www.bbc.co.uk /dna/h2g2/pda/A1315856?s_id=4&s_split=1 (183 words)

	McGraw-Hill AccessScience: Fermi-Dirac statistics
		It was later shown by P. Dirac that this form of statistics is also obtained when the total wave function of the system is antisymmetrical.
		This description was first given by E. Fermi, who applied the Pauli exclusion principle to the translational energy levels of a system of electrons.
		he statistical description of particles or systems of particles that satisfy the Pauli exclusion principle.
	www.accessscience.com /Encyclopedia/2/25/Est_253300_frameset.html (131 words)

	intro.html
		These are the exact formulae for electron and hole concentrations, according to the Fermi-Dirac statistics.
		The applet demonstrates the discrepancy in electron (or hole in p-type) concentration between the approximate formula [Maxwell-Boltzman approximation] and the full, accurate formula [Fermi-Dirac formula] when the concentration is high.
		In the classroom, the electron concentration, n, is expressed in terms of the Fermi level position, E
	jas.eng.buffalo.edu /education/semicon/fermi/heavyVSmoderate/intro.html (258 words)

	P. A. M. DIRAC
		Treated the problem of identical particles in quantum mechanics in 1926, gave the theoretical basis for the Bose-Einstein and Fermi (-Dirac) statistics developed earlier using the old quantum physics.
		(Quantum mechanical basis of Bose-Einstein and Fermi-Dirac statistics.)
		Developed the Dirac equation and the relativistic quantum mechanics of the electron, 1928.
	theory1.physics.wisc.edu /~ldurand/715html/courseinfo/biographies/dirac.html (224 words)

	P45
		Limiting cases of this equation are: Henry's law (MaxwellBoltzmann statistics); Langmuir's equation (Fermi-Dirac statistics); the equation which is alternative to Flory-Huggins model for sorption in rubbery polymers (BoseEinstein statistics); classical DMSM, which includes both types of quantum statistics with degeneration of the Bose-Enstein distribution into the Maxwell-Boltzmann one at moderate pressures.
		Thus, two types of sorption centers in polymers are suggested which are distinctive from each other by type of statistics (Fermi or Bose) in the process of interaction between sorbate and polymer.
		We have classical Maxwell-Boltzmann statistics and linear sorption isotherm at low filling in both modes.
	www.che.utexas.edu /nams/NAMS97_Abs/Posters/P45.html (358 words)

	Fermi-Dirac Statistics
		Next: Derivation of Fermi-Dirac Statistics Up: Derivation of Fermi-Dirac Statistics Previous: Derivation of Fermi-Dirac Statistics
		Instead, we derive the general form of these functions, called the Fermi-Dirac statistic:
		The appearance of the constant kT in the above formulas requires a study of statistical thermodynamics that is beyond the scope of these notes.
	cooper.edu /engineering/projects/gateway/ee/solidmat/modlec2/node2.html (127 words)

	On Fermi's route to Fermi-Dirac statistics
		Contrary to current opinion, Fermi did not introduce his quantum statistics in order to explain metal conductivity.
		His aim was to obtain a correct derivation of Sackur and Tetrode's formula for the entropy of a perfect monatomic gas.
	stacks.iop.org /0143-0807/15/102 (178 words)

	Maxwell Demon's Glossary
		Fermi-Dirac statistics - The behavior of any number of identical fermions (entities with half-odd spin).
		Probability for particles to end up in the same state is increased compared to Maxwell-Boltzmann statistics, cf.
		Bose-Einstein statistics - The behavior of any number of identical bosons (entities with whole number spin).
	www.maxwellian.demon.co.uk /faq/glossary.html (894 words)

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In the News (Wed 16 Dec 09)