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Topic: Bose Einstein statistics

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Identical particles

Boltzmann factor

Quantum field theory

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Stirling number

Boson

Pauli exclusion principle

Boltzmann distribution

Parastatistics

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Satyendra Nath Bose

Einstein

Boltzmann constant

	Albert Einstein - Wikipedia, the free encyclopedia
		Einstein divorced Mileva on February 14, 1919, and married his cousin Elsa Löwenthal (born Einstein: Löwenthal was the surname of her first husband, Max) on June 2, 1919.
		Einstein also assisted Erwin Schrödinger in the development of the quantum Boltzmann distribution, a mixed classical and quantum mechanical gas model although he realized that this was less significant than the Bose-Einstein model and declined to have his name included on the paper.
		Einstein began to form a generalized theory of gravitation with the Universal Law of Gravitation and the electromagnetic force in his first attempt to demonstrate the unification and simplification of the fundamental forces.
	en.wikipedia.org /wiki/Einstein (5456 words)

	Bose-Einstein statistics - Wikipedia, the free encyclopedia
		In statistical mechanics, Bose-Einstein statistics determines the statistical distribution of identical indistinguishable bosons over the energy states in thermal equilibrium.
		B-E statistics was introduced for photons in 1920 by Bose and generalized to atoms by Einstein in 1924.
		Einstein's original sketches were recovered in August 2005 in the Academical Library of Leiden, the Netherlands, where they were found by a student (Rowdy Boeyink).
	en.wikipedia.org /wiki/Bose-Einstein_statistics (560 words)

	Bose-Einstein condensate - Wikipedia, the free encyclopedia
		This phenomenon was predicted in the 1920s by Satyendra Nath Bose and Albert Einstein, based on Bose's work on the statistical mechanics of photons, which was then formalized and generalized by Einstein.
		The result of the efforts of Bose and Einstein is the concept of a Bose gas, governed by the Bose-Einstein statistics, which describes the statistical distribution of certain types of identical particles now known as bosons.
		Einstein speculated that cooling bosonic atoms to a very low temperature would cause them to fall (or "condense") into the lowest accessible quantum state, resulting in a new form of matter.
	en.wikipedia.org /wiki/Bose-Einstein_condensate (1140 words)

	J.C. Bose: 60 GHz in the 1890s
		Bose's experiments were carried out at the Presidency College in Calcutta, although for demonstrations he developed a compact portable version of the equipment, including transmitter, receiver and various microwave components.
		Bose was able to measure the wavelength of his radiation with a reflecting diffraction grating made of metal strips [7].
		Bose noted that the junction does not obey Ohm's law, and that there is a knee in the curve at approximately 0.45 volts; the junction becomes most effective at detection of short wavelength radiation when the corresponding bias voltage is applied.
	www.tuc.nrao.edu /~demerson/bose/bose.html (2868 words)

	AllRefer.com - statistical mechanics (Physics) - Encyclopedia
		statistical mechanics, quantitative study of systems consisting of a large number of interacting elements, such as the atoms or molecules of a solid, liquid, or gas, or the individual quanta of light (see photon) making up electromagnetic radiation.
		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.
		Statistical mechanics has also yielded deep insights in the understanding of magnetism, phase transitions, and superconductivity.
	reference.allrefer.com /encyclopedia/S/statmech.html (463 words)

	Bose (Site not responding. Last check: 2007-10-07)
		Bose was appointed as a Reader in physics at the University of Dacca in 1921 and taught there until 1945, being a professor and head of the physics department from 1927.
		Einstein extended Bose's treatment to material particles whose number is conserved and published several papers on this extension.
		Bose's shock of white hair and friendly personality was probably last in evidence ant a public function in January of this year, when an international symposium on statistical physics was held in Calcutta.
	www-groups.dcs.st-andrews.ac.uk /~history/Mathematicians/Bose.html (890 words)

	Reluctant Father
		Albert Einstein's equations of gravity are the foundation of the modern view of fl holes; ironically, he used the equations in trying to prove these objects cannot exist.
		Although Einstein's reasoning is correct, his point is irrelevant: it does not matter that a collapsing star at the Schwarzschild radius is unstable, because the star collapses past that radius anyway.
		Einstein's 1939 rejection of fl hole- to which Oppenheimer and his students were certainly oblivious, for they were working concurrently, 3,000 miles away-was of no relevance.
	www.fortunecity.com /emachines/e11/86/reluct.html (3471 words)

	ScienceWeek
		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.
		Einstein developed the idea to apply to other kinds of particle, not just to a 'gas' of photons, which is why this approach is usually referred to as '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.
	scienceweek.com /2003/sw030404.htm (10906 words)

	CERN Courier - Bose-Einstein condensation r - IOP Publishing - article
		Bose had not predicted this because he was looking at photons, which can simply disappear when the energy of the system is decreased.
		Satyendra Nath Bose was born in Calcutta, the son of a railway worker.
		A "boson" is a particle of integer spin that obeys Bose-Einstein statistics and is the counterpart of a "fermion", which is a particle of half-integer spin that obeys Fermi-Dirac statistics.
	www.cerncourier.com /main/article/41/10/17 (1452 words)

	Bose-Einstein condensate - ArtPolitic Encyclopedia of Politics : Information Portal
		This is the description of the statistics of identical particles that don't mind sharing an quantum energy level with each other (as opposed to Fermi Dirac statistics which describes identical particles of which you can only put one in each energy level).
		One of the results that one can derive from this statistics is the existense of stimulated emission of photons, which is the effect that is used in creating lasers.
		Einstein also applied the statistics to atoms instead of photons, and discovered that at a certain very low temperature, all of the atoms tend to drop into the lowest accessible energy level.
	www.artpolitic.org /infopedia/be/BEC.html (569 words)

	Bose-Einstein condensate (Site not responding. Last check: 2007-10-07)
		Einstein formalized and generalized these ideas and the result of their efforts is the so called Bose Einstein statistics.
		This is the description of the statistics of identical particles that don't mind sharing a quantum energy level with each other (as opposed to Fermi Dirac statistics which describe identical particles of which you can only put one in each energy level).
		One of the results that one can derive from this statistics is the existence of stimulated emission of photons, which is the effect that is used in creating lasers.
	usapedia.com /b/bose-einstein-condensate.html (520 words)

	Bose-Einstein condensate - SmartyBrain Encyclopedia and Dictionary (Site not responding. Last check: 2007-10-07)
		They were predicted in the 1920s by Satyendra Nath Bose and Albert Einstein based on Bose's work on rules for deciding when two photons should be counted up as either identical or different; Einstein formalized and generalized these ideas, and the result of their efforts is the so called Bose Einstein statistics.
		This is the description of the statistics of identical particles that can share a quantum energy level with each other (as opposed to Fermi Dirac statistics, which describe identical particles of which you can only put one in each energy level).
		One of the results that one can derive from these statistics is the existence of stimulated emission of photons, which is the effect that is used in creating lasers.
	smartybrain.com /index.php/Bose-Einstein_condensate (809 words)

	Bose-Einstein (Site not responding. Last check: 2007-10-07)
		Satyendranath Bose was born in Calcutta in 1894 and was 80 years old when he died in Calcutta in 1974.
		Using the particle picture of Einstein, Bose was able to derive the radiation formula by systematically developing a statistics of massless particles without the constraint of particle number conservation.
		Einstein was so happy with Bose's work that he translated the manuscript into German and arranged its publication in Zeitschrift f.
	www.physics.umd.edu /robot/einstein/bose.html (545 words)

	No. 1893: Satyendranath Bose
		Einstein carried on a vast correspondence with the whole spec-trum of brilliance to crankery.
		Bose had shown how Planck's and Einstein's work were consistent with one another.
		Bose went to Europe to work as part of the group that now put quantum mechanics on solid footing.
	www.uh.edu /engines/epi1893.htm (523 words)

	Bose-Einstein statistics -- Encyclopædia Britannica
		The aggregation of particles in the same state, which is characteristic of particles obeying Bose-Einstein statistics, accounts for the cohesive streaming of laser light and the frictionless creeping of superfluid helium.
		Statistics appear in the claims of advertisers, in predictions of election results and opinion polls, in cost-of-living indexes, and in reports of business...
		Einstein's work led to such scientific advances as the control of atomic energy and to some of the investigations of space currently being...
	www.britannica.com /eb/article-9080807?tocId=9080807&query=einstein&ct= (884 words)

	BEC - What is it and where did the idea come from?
		Satyendra Nath Bose was studying the new idea (at that time) that the light came in little discrete packets (we now call these "quanta" or "photons").
		Bose had trouble getting people to believe him and to publish his ideas in the scientific magazines of the day, so he sent them to Einstein.
		Einstein liked them, and he was a very important scientist at that time, so he used his influence to get them published.
	www.colorado.edu /physics/2000/bec/what_is_it.html (786 words)

	Boson (Site not responding. Last check: 2007-10-07)
		Bosons are subatomic particles that possess integer spin (i.e., angular momentum in integer units.) and are governed by Bose-Einstein statistics.
		In 1924, Satyendra Nath Bose (1894-1974) published a paper "Planck's Law and the Hypothesis of Light Quanta" which led Albert Einstein (1879-1955) to seek him out for collaboration in developing a theory regarding the gas like qualities of electromagnetic radiation.
		In Fermi-Dirac and Bose-Einstein statistics "y" is a function of temperature and particle concentration,.
	home.earthlink.net /~tdp/boson.html (257 words)

	Profile of the month (Site not responding. Last check: 2007-10-07)
		It was during this period that he wrote the famous paper on the statistics of photons.
		Einstein generalized it to the counting of states of atoms, and predicted the phenomena of Bose-Einstein condensation, which has now been experimentally confirmed.
		Einstein, who saw at once that Bose had removed a major objection against light quanta, enthusiastically endorsed his work.
	www.ewh.ieee.org /r10/bombay/news3/page9.html (390 words)

	Chapter 9. (Site not responding. Last check: 2007-10-07)
		In statistical systems one obvious parameter of dimension of length is the average distance between particles.
		For Bose-Einstein statistics the normalization of the distribution is equivalent to the determination of the chemical potential.
		Einstein proposed that at low temperature interactions among atoms cannot be neglected.
	www.physics.uc.edu /suranyi/Modern_physics/Lecture_Notes/modern_physics9.html (3904 words)

	Calcuttaweb - People : Satyendra Nath Bose
		Bose was thus able to mould his career and later shine in life.
		Bose served in Dacca University nearly twenty-five years as Professor teacher he was admired by his students was friendly and helpful to his colleagues.
		The death of Bose was a great loss not only to India but also to the whole world and especially to the world of science.
	www.calcuttaweb.com /people/snbose.shtml (3052 words)

	Chip off the old steel (Site not responding. Last check: 2007-10-07)
		The inter-action between Bose, who was born in Kolkata in 1894 and died in 1974, and Einstein appears to have changed the course of physics.
		Einstein acceded to Bose’s request to allow him to translate the great man’s paper on General Relativity from German into English for readers in India even though a London publisher had wanted to assert his copyright.
		Einstein was convinced by Bose’s work (“the Indian Bose has given a beautiful derivation of Planck’s law”) and secured its publication in Europe after personally translating it into German.
	web.mid-day.com /columns/amit_roy/2005/january/101584.htm (985 words)

	Bose-Einstein correlations - an introduction (Site not responding. Last check: 2007-10-07)
		Considering identical and indistinguishable particles, the theory of quantum statistics differentiates two kinds of particles, according to the way in which they may be distributed among the available wave functions associated with each energy state.
		The statistics which concerns particles satisfying the exclusion principle ad hence described by antisymmetric wave functions, is called Fermi-Dirac statistics, and the particles are called fermions.
		The second kind of statistics was first studied in 1921 by indian mathematician and physicist Satyendra Nath Bose in a paper on the statistics of photons.
	www.hep.lu.se /delphi/be/beintro.html (554 words)

	Articles - Satyendra Nath Bose (Site not responding. Last check: 2007-10-07)
		While at University of Dhaka, Bose wrote a short article called Planck's Law and the Hypothesis of Light Quanta, describing the photoelectric effect and based on a lecture he had given on the ultraviolet catastrophe.
		The error was a simple mistake that would appear obviously wrong to anyone with a basic understanding of statistics, and similar to arguing that flipping two fair coins will produce two heads one-third of the time.
		Bose's ideas were afterward well received in the world of physics, and he was granted leave from the University of Dacca to travel to Europe in 1924.
	www.gaple.com /articles/Satyendra_Nath_Bose (626 words)

	Bose gas (Site not responding. Last check: 2007-10-07)
		It is composed of bosons, which have an integral value of spin, and obey Bose-Einstein statistics.
		The statistical mechanics of bosons were developed by Satyendra Nath Bose for photons, and extended to massive particles by Albert Einstein who realized that an ideal gas of bosons would form a condensate at a low enough temperature, unlike a classical ideal gas.
		The problem with this continuum approximation for a Bose gas is that the ground state has been effectively ignored, giving a degeneracy of zero for zero energy.
	www.worldhistory.com /wiki/B/Bose-gas.htm (1171 words)

	Bose-Einstein statistics
		This explain why, at low temperatures, bosons can behave very differently than fermions; all the particules they will tend to congregate together at the same lowest-energy state, forming what is a Bose-Einstein condensate.
		The distribution function f(E) is the probability that a particle is in energy state E, for B-E statistics the following hold:
		The text of this article is licensed under the GFDL.
	www.ebroadcast.com.au /lookup/encyclopedia/bo/Bose_Einstein_statistics.html (182 words)

	Ideal Bose gas (Site not responding. Last check: 2007-10-07)
		Satyendra Nath Bose (January 1, 1894 - February 4, 1974) was an Indian physicist specializing in mathematical physics.
		Einstein adopted the idea, extended on atoms and predicted the existence of phenomena called later as Bose-Einstein condensate.
		Bose-Einstein statistics and bosons are called after Bose as well.
	gassystem.net (146 words)

	Einstein's Guidance (Site not responding. Last check: 2007-10-07)
		Bose sent another article in 1926 to Einstein relating to the same topic.
		Einstein translated this article into German but also expressed some doubts and points of disagreement.
		Bose felt it would be more appropriate to meet the great scientist Einstein and discuss the paper with him than to correspond with him.
	www.freeindia.org /biographies/greatscientists/sathyendranathbose/page10.htm (270 words)

	Einstein/Boise Theory
		The coins are different by virtue (and only by virtue) of the fact that one is flipped before the other, and we know which one that is. That is, it is our knowledge of the history of the objects that allows us to tell them apart, even if they look identical.
		All objects you see around you follow Bolzmann statistics, because even if you can't tell them apart by looking at them, you can always tell them apart by discovering their history, which will be unique for each object.
		The ending-up-in-one-situation is called a ``Bose condensation'', and it makes the news because it surprises human beings, whose intuition is to always see Boltzmann statistics.
	www.newton.dep.anl.gov /askasci/phy99/phy99x83.htm (825 words)

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