Normal coordinates - Revision history

en>TakuyaMurata: /* Geodesic normal coordinates */

2014-12-06T07:43:24Z

Geodesic normal coordinates

← Older revision		Revision as of 09:43, 6 December 2014
Line 1:		Line 1:
	~~{{Infobox scientist~~		Emilia Shryock is my name but you can call me anything you like. North Dakota is her beginning location but she will have to move one working day or an additional. I used to be unemployed but now I am a librarian and the salary has been really satisfying. To gather coins is a thing that I'm totally addicted to.<br><br>Look at my homepage - at home std testing ([http://xrambo.com/user/NEme Read More In this article])
	~~\| name = Professor Edmund Stoner~~
	~~\| birth_name = Edmund Clifton Stoner~~
	~~\| native_name_lang =~~
	~~\| image = <!--(as myimage.jpg, no 'File:')-->~~
	~~\| image_size =~~
	~~\| alt =~~
	~~\| caption =~~
	~~\| birth_date = {{Birth date\|1899\|11\|02}}~~
	~~\| birth_place = [[Surrey]], [[England]]~~
	~~\| death_date ={{Death date and age\|1968\|12\|27\|1899\|11\|02}}~~
	~~\| death_place = [[Leeds]], [[England]]<ref name="frs"/>~~
	~~\| resting_place =~~
	~~\| resting_place_coordinates = <!-- {{Coord\|LAT\|LONG\|type:landmark\|display=inline,title}} -->~~
	~~\| other_names =~~
	~~\| residence =~~
	~~\| citizenship =~~
	~~\| nationality =~~
	~~\| fields =~~
	~~\| workplaces = [[University of Leeds]]~~
	~~\| alma_mater = [[University of Cambridge]]~~
	~~\| thesis_title =~~
	~~\| thesis_url =~~
	~~\| thesis_year =~~
	~~\| doctoral_advisor =~~
	~~\| academic_advisors =~~
	~~\| doctoral_students =~~
	~~\| notable_students =~~
	~~\| known_for = [[Ferromagnetism]]~~
	~~\| author_abbrev_bot =~~
	~~\| author_abbrev_zoo =~~
	~~\| influences =~~
	~~\| influenced =~~
	~~\| awards = [[Fellow of the Royal Society]]<ref name="frs">{{cite doi\|10.1098/rsbm.1969.0011}}</ref>~~
	~~\| signature = <!--(filename only)-->~~
	~~\| signature_alt =~~
	~~\| website = <!-- {{URL\|www.example.com}} -->~~
	~~\| footnotes =~~
	~~\| spouse =~~
	~~\| children =~~
	}}'''Edmund Clifton Stoner''' [[Royal Society\|FRS]] (October 2, 1899 – December 27, 1968) was a [[United Kingdom\|British]] theoretical [[physicist]]. He is principally known for his work on the origin and nature of itinerant ferro[[magnetism]] (the type of ferromagnetic behavior associated with pure transition metals like cobalt, nickel, and iron), including the collective electron theory of [[ferromagnetism]] and the [[Stoner criterion]] for [[ferromagnetism]].<ref>{{cite doi\|10.1098/rspa.1939.0003}}</ref><ref>{{cite doi\|10.1098/rspa.1938.0066}}</ref><ref>{{cite doi\|10.1098/rspa.1936.0075}}</ref><ref>{{cite doi\|10.1098/rspa.1935.0214}}</ref><ref>{{cite doi\|10.1098/rspa.1925.0026}}</ref><ref>{{cite doi\|10.1098/rspa.1924.0050}}</ref><ref>{{cite news\|journal=J. for the History of Astronomy\|author=Nauenberg, Michael\|title=Edmund C. Stoner and the Discovery of the Maximum Mass of White Dwarfs\|volume=xxxix\|year=2008\|url=http://physics.ucsc.edu/~michael/stonerchandra.pdf}}</ref>

	~~==Biography==~~
	Stoner was born in Esher, Surrey, the son of cricketer [[Arthur Stoner\|Arthur Hallett Stoner]]. He won a scholarship to [[Bolton School]] (1911–1918) and then attended [[University of Cambridge]] in 1918, graduating in 1921. After graduation, he worked at the [[Cavendish Laboratory]] on the absorption of [[X-rays]] by matter and [[electron]] energy levels; his 1924 paper on this subject prefigured the [[Pauli exclusion principle]].{{citation needed\|date=August 2013}} Stoner was appointed a Lecturer in the Department of [[Physics]] at the [[University of Leeds]] in 1932, becoming [[Professor]] of Theoretical Physics there in 1939. He did some early work in [[astrophysics]] and computed a [[Chandrasekhar limit#History\|limit]] for the mass of white dwarf stars in 1930. Most of his research, however, was on [[magnetism]], where, starting in 1938, he developed the collective electron theory of [[ferromagnetism]]. He retired in 1963.

	~~==Awards==~~
	~~The E C Stoner building at the [[University of Leeds]]~~ is named after him.<ref name="frs"/><ref name="leedsbio">[http://www.stoner.leeds.ac.uk/about/stoner Edmund Clifton Stoner], web page at the [[University of Leeds]], accessed December 21, 2008.</ref><sup>,</sup><ref name~~="paperlist">[http://www.leeds.ac.uk/library/spcoll/handlists/062MS696Stoner.pdf List of papers], collection at the Leeds University Library, accessed January 18, 2007.</ref>~~

	He was elected a [[Fellow of the Royal Society]] in May 1937.<ref>{{cite web \| url= http://www2.royalsociety.org/DServe/dserve.exe?dsqIni=Dserve.ini&dsqApp=Archive&dsqCmd=Show.tcl&dsqDb=Persons&dsqPos=0&dsqSearch=%28Surname%3D%27stoner%27%29\| title = Library and Archive Catalogue\|publisher= Royal Society\| accessdate= 22 October 2010}}</ref>

	~~Stoner had been diagnosed with [[diabetes]] in 1919. He controlled it with diet until 1927, when [[insulin]] treatment became available.<ref name="frs" />~~

	~~==Stoner model of ferromagnetism==~~

	[[File:Stoner model of ferromagnetism.svg\|thumb\|260px\|right\|A schematic band structure for the Stoner model of ferromagnetism. An exchange interaction has split the energy of states with different spins, and states near the Fermi level are spin-polarized.]][[Electronic band structure\|Electron bands]] can ~~spontaneously split into up and down spins~~. ~~This happens if the relative gain in [[exchange interaction]] (the interaction of electrons via the Pauli exclusion principle)~~ is ~~larger than the loss in kinetic energy~~.

	~~:<math>~~
	~~\epsilon_{\uparrow} (k) = \epsilon_0 (k) +~~ I ~~\frac{n_{\uparrow}-n_{\downarrow}}{n}~~
	~~</math>~~

	~~:<math>~~
	~~\epsilon_{\downarrow} (k) = \epsilon_0 (k) -~~ I ~~\frac{n_\uparrow-n_{\downarrow}}{n}~~
	~~</math>~~
	~~where <math>\epsilon_0 (k)</math> is the energy of the metal before exchange effects are included, <math>\epsilon_{\uparrow}</math>~~ and ~~<math>\epsilon_{\downarrow}</math> are~~ the ~~energies of the spin up and down electron bands respectively~~. ~~The Stoner parameter which~~ is a ~~measure of the strength of the exchange correlation is denoted <math>~~I~~</math>, the number of electrons is <math> n = n_{\uparrow} + n_{\downarrow} </math>~~. ~~Finally~~ <~~math~~> k <~~/math~~> ~~is the [[wavenumber]] as the electrons bands are in wavenumber~~-space. If more electrons favour one of the states this will create [[magnetism]]. The electrons obey [[Fermi–Dirac statistics]] so when the above formulas are summed over all <math>k</math>-space then the [[Stoner criterion]] for ferromagnetism can be established.

	~~==Selected publications==~~
	* The distribution of electrons among atomic levels, ''Philosophical Magazine'' (~~6th series) '''48''' (1924), pp. 719–736.~~
	* The limiting density of white dwarf stars, ''Philosophical Magazine'' (7th series) '''7''' (1929), pp. 63–70.
	* The equilibrium of dense stars, ''Philosophical Magazine'' (7th series) '''9''' (1930), pp. 944–963.
	* ''Magnetism and atomic structure'', London: Methuen, 1926.
	* ''Magnetism and matter'', London: Methuen, 1934.
	* Collective electron ferromagnetism in metals and alloys, ''Journal de physique et le radium'' (8th series) '''12''' (1951), pp. 372–388.

	~~==References==~~
	~~{{Reflist}}~~

	~~==Further reading==~~
	*[http://~~igorbarsukov~~.com/~~stoner.html Demonstrative derivation of the Stoner Criterion]~~

	~~{{Authority control\|VIAF=5323347}}~~

	~~{{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->~~
	~~\| NAME = Stoner, Edmund~~
	~~\| ALTERNATIVE NAMES =~~
	~~\| SHORT DESCRIPTION = British physicist~~
	~~\| DATE OF BIRTH = October 2, 1899~~
	~~\| PLACE OF BIRTH = [[Surrey]], [[England]]~~
	~~\| DATE OF DEATH = December 27, 1968~~
	~~\| PLACE OF DEATH = [[Leeds]], [[England]]~~
	}}
	~~{{DEFAULTSORT:Stoner, Edmund}}~~
	~~[[Category:1899 births]]~~
	~~[[Category:1968 deaths]]~~
	~~[[Category:People from Esher]]~~
	~~[[Category:English physicists]]~~
	~~[[Category:Academics of the University of Leeds]]~~
	~~[[Category:Fellows of the Royal Society]~~]

en>Addbot: Bot: Migrating 2 interwiki links, now provided by Wikidata on d:q2152232

2013-03-16T07:23:56Z

Bot: Migrating 2 interwiki links, now provided by Wikidata on d:q2152232

← Older revision		Revision as of 09:23, 16 March 2013
Line 1:		Line 1:
	The ~~title~~ of [http://www.~~hotporn123~~.~~com~~/~~user~~/~~RPocock over~~ the ~~counter std test~~] ~~author~~ is ~~Numbers~~. ~~North Dakota~~ is ~~our beginning location~~. ~~Hiring~~ is ~~my profession~~. ~~To collect cash~~ is one of the ~~things I love most~~.		{{Infobox scientist
			\| name = Professor Edmund Stoner
			\| birth_name = Edmund Clifton Stoner
			\| native_name_lang =
			\| image = <!--(as myimage.jpg, no 'File:')-->
			\| image_size =
			\| alt =
			\| caption =
			\| birth_date = {{Birth date\|1899\|11\|02}}
			\| birth_place = [[Surrey]], [[England]]
			\| death_date ={{Death date and age\|1968\|12\|27\|1899\|11\|02}}
			\| death_place = [[Leeds]], [[England]]<ref name="frs"/>
			\| resting_place =
			\| resting_place_coordinates = <!-- {{Coord\|LAT\|LONG\|type:landmark\|display=inline,title}} -->
			\| other_names =
			\| residence =
			\| citizenship =
			\| nationality =
			\| fields =
			\| workplaces = [[University of Leeds]]
			\| alma_mater = [[University of Cambridge]]
			\| thesis_title =
			\| thesis_url =
			\| thesis_year =
			\| doctoral_advisor =
			\| academic_advisors =
			\| doctoral_students =
			\| notable_students =
			\| known_for = [[Ferromagnetism]]
			\| author_abbrev_bot =
			\| author_abbrev_zoo =
			\| influences =
			\| influenced =
			\| awards = [[Fellow of the Royal Society]]<ref name="frs">{{cite doi\|10.1098/rsbm.1969.0011}}</ref>
			\| signature = <!--(filename only)-->
			\| signature_alt =
			\| website = <!-- {{URL\|www.example.com}} -->
			\| footnotes =
			\| spouse =
			\| children =
			}}'''Edmund Clifton Stoner''' [[Royal Society\|FRS]] (October 2, 1899 – December 27, 1968) was a [[United Kingdom\|British]] theoretical [[physicist]]. He is principally known for his work on the origin and nature of itinerant ferro[[magnetism]] (the type of ferromagnetic behavior associated with pure transition metals like cobalt, nickel, and iron), including the collective electron theory of [[ferromagnetism]] and the [[Stoner criterion]] for [[ferromagnetism]].<ref>{{cite doi\|10.1098/rspa.1939.0003}}</ref><ref>{{cite doi\|10.1098/rspa.1938.0066}}</ref><ref>{{cite doi\|10.1098/rspa.1936.0075}}</ref><ref>{{cite doi\|10.1098/rspa.1935.0214}}</ref><ref>{{cite doi\|10.1098/rspa.1925.0026}}</ref><ref>{{cite doi\|10.1098/rspa.1924.0050}}</ref><ref>{{cite news\|journal=J. for the History of Astronomy\|author=Nauenberg, Michael\|title=Edmund C. Stoner and the Discovery of the Maximum Mass of White Dwarfs\|volume=xxxix\|year=2008\|url=http://physics.ucsc.edu/~michael/stonerchandra.pdf}}</ref>

			==Biography==
			Stoner was born in Esher, Surrey, the son of cricketer [[Arthur Stoner\|Arthur Hallett Stoner]]. He won a scholarship to [[Bolton School]] (1911–1918) and then attended [[University of Cambridge]] in 1918, graduating in 1921. After graduation, he worked at the [[Cavendish Laboratory]] on the absorption of [[X-rays]] by matter and [[electron]] energy levels; his 1924 paper on this subject prefigured the [[Pauli exclusion principle]].{{citation needed\|date=August 2013}} Stoner was appointed a Lecturer in the Department of [[Physics]] at the [[University of Leeds]] in 1932, becoming [[Professor]] of Theoretical Physics there in 1939. He did some early work in [[astrophysics]] and computed a [[Chandrasekhar limit#History\|limit]] for the mass of white dwarf stars in 1930. Most of his research, however, was on [[magnetism]], where, starting in 1938, he developed the collective electron theory of [[ferromagnetism]]. He retired in 1963.

			==Awards==
			The E C Stoner building at the [[University of Leeds]] is named after him.<ref name="frs"/><ref name="leedsbio">[http://www.stoner.leeds.ac.uk/about/stoner Edmund Clifton Stoner], web page at the [[University of Leeds]], accessed December 21, 2008.</ref><sup>,</sup><ref name="paperlist">[http://www.leeds.ac.uk/library/spcoll/handlists/062MS696Stoner.pdf List of papers], collection at the Leeds University Library, accessed January 18, 2007.</ref>

			He was elected a [[Fellow of the Royal Society]] in May 1937.<ref>{{cite web \| url= http://www2.royalsociety.org/DServe/dserve.exe?dsqIni=Dserve.ini&dsqApp=Archive&dsqCmd=Show.tcl&dsqDb=Persons&dsqPos=0&dsqSearch=%28Surname%3D%27stoner%27%29\| title = Library and Archive Catalogue\|publisher= Royal Society\| accessdate= 22 October 2010}}</ref>

			Stoner had been diagnosed with [[diabetes]] in 1919. He controlled it with diet until 1927, when [[insulin]] treatment became available.<ref name="frs" />

			==Stoner model of ferromagnetism==

			[[File:Stoner model of ferromagnetism.svg\|thumb\|260px\|right\|A schematic band structure for the Stoner model of ferromagnetism. An exchange interaction has split the energy of states with different spins, and states near the Fermi level are spin-polarized.]][[Electronic band structure\|Electron bands]] can spontaneously split into up and down spins. This happens if the relative gain in [[exchange interaction]] (the interaction of electrons via the Pauli exclusion principle) is larger than the loss in kinetic energy.

			:<math>
			\epsilon_{\uparrow} (k) = \epsilon_0 (k) + I \frac{n_{\uparrow}-n_{\downarrow}}{n}
			</math>

			:<math>
			\epsilon_{\downarrow} (k) = \epsilon_0 (k) - I \frac{n_\uparrow-n_{\downarrow}}{n}
			</math>
			where <math>\epsilon_0 (k)</math> is the energy of the metal before exchange effects are included, <math>\epsilon_{\uparrow}</math> and <math>\epsilon_{\downarrow}</math> are the energies of the spin up and down electron bands respectively. The Stoner parameter which is a measure of the strength of the exchange correlation is denoted <math>I</math>, the number of electrons is <math> n = n_{\uparrow} + n_{\downarrow} </math>. Finally <math> k </math> is the [[wavenumber]] as the electrons bands are in wavenumber-space. If more electrons favour one of the states this will create [[magnetism]]. The electrons obey [[Fermi–Dirac statistics]] so when the above formulas are summed over all <math>k</math>-space then the [[Stoner criterion]] for ferromagnetism can be established.

			==Selected publications==
			* The distribution of electrons among atomic levels, ''Philosophical Magazine'' (6th series) '''48''' (1924), pp. 719–736.
			* The limiting density of white dwarf stars, ''Philosophical Magazine'' (7th series) '''7''' (1929), pp. 63–70.
			* The equilibrium of dense stars, ''Philosophical Magazine'' (7th series) '''9''' (1930), pp. 944–963.
			* ''Magnetism and atomic structure'', London: Methuen, 1926.
			* ''Magnetism and matter'', London: Methuen, 1934.
			* Collective electron ferromagnetism in metals and alloys, ''Journal de physique et le radium'' (8th series) '''12''' (1951), pp. 372–388.

			==References==
			{{Reflist}}

			==Further reading==
			*[http://igorbarsukov.com/stoner.html Demonstrative derivation of the Stoner Criterion]

			{{Authority control\|VIAF=5323347}}

			{{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
			\| NAME = Stoner, Edmund
			\| ALTERNATIVE NAMES =
			\| SHORT DESCRIPTION = British physicist
			\| DATE OF BIRTH = October 2, 1899
			\| PLACE OF BIRTH = [[Surrey]], [[England]]
			\| DATE OF DEATH = December 27, 1968
			\| PLACE OF DEATH = [[Leeds]], [[England]]
			}}
			{{DEFAULTSORT:Stoner, Edmund}}
			[[Category:1899 births]]
			[[Category:1968 deaths]]
			[[Category:People from Esher]]
			[[Category:English physicists]]
			[[Category:Academics of the University of Leeds]]
			[[Category:Fellows of the Royal Society]]

en>Helpful Pixie Bot: ISBNs (Build KF)

2012-05-08T10:31:52Z

ISBNs (Build KF)

New page

The title of [http://www.hotporn123.com/user/RPocock over the counter std test] author is Numbers. North Dakota is our beginning location. Hiring is my profession. To collect cash is one of the things I love most.

← Older revision		Revision as of 09:43, 6 December 2014
Line 1:		Line 1:
	~~{{Infobox scientist~~		Emilia Shryock is my name but you can call me anything you like. North Dakota is her beginning location but she will have to move one working day or an additional. I used to be unemployed but now I am a librarian and the salary has been really satisfying. To gather coins is a thing that I'm totally addicted to.<br><br>Look at my homepage - at home std testing ([http://xrambo.com/user/NEme Read More In this article])
	~~\| name = Professor Edmund Stoner~~
	~~\| birth_name = Edmund Clifton Stoner~~
	~~\| native_name_lang =~~
	~~\| image = <!--(as myimage.jpg, no 'File:')-->~~
	~~\| image_size =~~
	~~\| alt =~~
	~~\| caption =~~
	~~\| birth_date = {{Birth date\|1899\|11\|02}}~~
	~~\| birth_place = [[Surrey]], [[England]]~~
	~~\| death_date ={{Death date and age\|1968\|12\|27\|1899\|11\|02}}~~
	~~\| death_place = [[Leeds]], [[England]]<ref name="frs"/>~~
	~~\| resting_place =~~
	~~\| resting_place_coordinates = <!-- {{Coord\|LAT\|LONG\|type:landmark\|display=inline,title}} -->~~
	~~\| other_names =~~
	~~\| residence =~~
	~~\| citizenship =~~
	~~\| nationality =~~
	~~\| fields =~~
	~~\| workplaces = [[University of Leeds]]~~
	~~\| alma_mater = [[University of Cambridge]]~~
	~~\| thesis_title =~~
	~~\| thesis_url =~~
	~~\| thesis_year =~~
	~~\| doctoral_advisor =~~
	~~\| academic_advisors =~~
	~~\| doctoral_students =~~
	~~\| notable_students =~~
	~~\| known_for = [[Ferromagnetism]]~~
	~~\| author_abbrev_bot =~~
	~~\| author_abbrev_zoo =~~
	~~\| influences =~~
	~~\| influenced =~~
	~~\| awards = [[Fellow of the Royal Society]]<ref name="frs">{{cite doi\|10.1098/rsbm.1969.0011}}</ref>~~
	~~\| signature = <!--(filename only)-->~~
	~~\| signature_alt =~~
	~~\| website = <!-- {{URL\|www.example.com}} -->~~
	~~\| footnotes =~~
	~~\| spouse =~~
	~~\| children =~~
	}}'''Edmund Clifton Stoner''' [[Royal Society\|FRS]] (October 2, 1899 – December 27, 1968) was a [[United Kingdom\|British]] theoretical [[physicist]]. He is principally known for his work on the origin and nature of itinerant ferro[[magnetism]] (the type of ferromagnetic behavior associated with pure transition metals like cobalt, nickel, and iron), including the collective electron theory of [[ferromagnetism]] and the [[Stoner criterion]] for [[ferromagnetism]].<ref>{{cite doi\|10.1098/rspa.1939.0003}}</ref><ref>{{cite doi\|10.1098/rspa.1938.0066}}</ref><ref>{{cite doi\|10.1098/rspa.1936.0075}}</ref><ref>{{cite doi\|10.1098/rspa.1935.0214}}</ref><ref>{{cite doi\|10.1098/rspa.1925.0026}}</ref><ref>{{cite doi\|10.1098/rspa.1924.0050}}</ref><ref>{{cite news\|journal=J. for the History of Astronomy\|author=Nauenberg, Michael\|title=Edmund C. Stoner and the Discovery of the Maximum Mass of White Dwarfs\|volume=xxxix\|year=2008\|url=http://physics.ucsc.edu/~michael/stonerchandra.pdf}}</ref>

	~~==Biography==~~
	Stoner was born in Esher, Surrey, the son of cricketer [[Arthur Stoner\|Arthur Hallett Stoner]]. He won a scholarship to [[Bolton School]] (1911–1918) and then attended [[University of Cambridge]] in 1918, graduating in 1921. After graduation, he worked at the [[Cavendish Laboratory]] on the absorption of [[X-rays]] by matter and [[electron]] energy levels; his 1924 paper on this subject prefigured the [[Pauli exclusion principle]].{{citation needed\|date=August 2013}} Stoner was appointed a Lecturer in the Department of [[Physics]] at the [[University of Leeds]] in 1932, becoming [[Professor]] of Theoretical Physics there in 1939. He did some early work in [[astrophysics]] and computed a [[Chandrasekhar limit#History\|limit]] for the mass of white dwarf stars in 1930. Most of his research, however, was on [[magnetism]], where, starting in 1938, he developed the collective electron theory of [[ferromagnetism]]. He retired in 1963.

	~~==Awards==~~
	~~The E C Stoner building at the [[University of Leeds]]~~ is named after him.<ref name="frs"/><ref name="leedsbio">[http://www.stoner.leeds.ac.uk/about/stoner Edmund Clifton Stoner], web page at the [[University of Leeds]], accessed December 21, 2008.</ref><sup>,</sup><ref name~~="paperlist">[http://www.leeds.ac.uk/library/spcoll/handlists/062MS696Stoner.pdf List of papers], collection at the Leeds University Library, accessed January 18, 2007.</ref>~~

	He was elected a [[Fellow of the Royal Society]] in May 1937.<ref>{{cite web \| url= http://www2.royalsociety.org/DServe/dserve.exe?dsqIni=Dserve.ini&dsqApp=Archive&dsqCmd=Show.tcl&dsqDb=Persons&dsqPos=0&dsqSearch=%28Surname%3D%27stoner%27%29\| title = Library and Archive Catalogue\|publisher= Royal Society\| accessdate= 22 October 2010}}</ref>

	~~Stoner had been diagnosed with [[diabetes]] in 1919. He controlled it with diet until 1927, when [[insulin]] treatment became available.<ref name="frs" />~~

	~~==Stoner model of ferromagnetism==~~

	[[File:Stoner model of ferromagnetism.svg\|thumb\|260px\|right\|A schematic band structure for the Stoner model of ferromagnetism. An exchange interaction has split the energy of states with different spins, and states near the Fermi level are spin-polarized.]][[Electronic band structure\|Electron bands]] can ~~spontaneously split into up and down spins~~. ~~This happens if the relative gain in [[exchange interaction]] (the interaction of electrons via the Pauli exclusion principle)~~ is ~~larger than the loss in kinetic energy~~.

	~~:<math>~~
	~~\epsilon_{\uparrow} (k) = \epsilon_0 (k) +~~ I ~~\frac{n_{\uparrow}-n_{\downarrow}}{n}~~
	~~</math>~~

	~~:<math>~~
	~~\epsilon_{\downarrow} (k) = \epsilon_0 (k) -~~ I ~~\frac{n_\uparrow-n_{\downarrow}}{n}~~
	~~</math>~~
	~~where <math>\epsilon_0 (k)</math> is the energy of the metal before exchange effects are included, <math>\epsilon_{\uparrow}</math>~~ and ~~<math>\epsilon_{\downarrow}</math> are~~ the ~~energies of the spin up and down electron bands respectively~~. ~~The Stoner parameter which~~ is a ~~measure of the strength of the exchange correlation is denoted <math>~~I~~</math>, the number of electrons is <math> n = n_{\uparrow} + n_{\downarrow} </math>~~. ~~Finally~~ <~~math~~> k <~~/math~~> ~~is the [[wavenumber]] as the electrons bands are in wavenumber~~-space. If more electrons favour one of the states this will create [[magnetism]]. The electrons obey [[Fermi–Dirac statistics]] so when the above formulas are summed over all <math>k</math>-space then the [[Stoner criterion]] for ferromagnetism can be established.

	~~==Selected publications==~~
	* The distribution of electrons among atomic levels, ''Philosophical Magazine'' (~~6th series) '''48''' (1924), pp. 719–736.~~
	* The limiting density of white dwarf stars, ''Philosophical Magazine'' (7th series) '''7''' (1929), pp. 63–70.
	* The equilibrium of dense stars, ''Philosophical Magazine'' (7th series) '''9''' (1930), pp. 944–963.
	* ''Magnetism and atomic structure'', London: Methuen, 1926.
	* ''Magnetism and matter'', London: Methuen, 1934.
	* Collective electron ferromagnetism in metals and alloys, ''Journal de physique et le radium'' (8th series) '''12''' (1951), pp. 372–388.

	~~==References==~~
	~~{{Reflist}}~~

	~~==Further reading==~~
	*[http://~~igorbarsukov~~.com/~~stoner.html Demonstrative derivation of the Stoner Criterion]~~

	~~{{Authority control\|VIAF=5323347}}~~

	~~{{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->~~
	~~\| NAME = Stoner, Edmund~~
	~~\| ALTERNATIVE NAMES =~~
	~~\| SHORT DESCRIPTION = British physicist~~
	~~\| DATE OF BIRTH = October 2, 1899~~
	~~\| PLACE OF BIRTH = [[Surrey]], [[England]]~~
	~~\| DATE OF DEATH = December 27, 1968~~
	~~\| PLACE OF DEATH = [[Leeds]], [[England]]~~
	}}
	~~{{DEFAULTSORT:Stoner, Edmund}}~~
	~~[[Category:1899 births]]~~
	~~[[Category:1968 deaths]]~~
	~~[[Category:People from Esher]]~~
	~~[[Category:English physicists]]~~
	~~[[Category:Academics of the University of Leeds]]~~
	~~[[Category:Fellows of the Royal Society]~~]