Finite potential well - Revision history

en>Timetraveler3.14 at 22:57, 14 November 2014

2014-11-14T22:57:33Z

← Older revision		Revision as of 00:57, 15 November 2014
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	~~In [[theoretical physics\|theoretical]] [[condensed matter physics]], '''Bosonization''~~' is a ~~mathematical procedure by which a system of interacting [[fermions]] in [[dimension\|(1+1) dimensions]] can be transformed~~ to a ~~system of massless, non-interacting [[bosons]]~~.~~<ref name=gogolin>{{cite book\|last=Gogolin\|first=Alexander O.\|title=Bosonization~~ and ~~Strongly Correlated Systems\|year=2004\|publisher=Cambridge University Press\|isbn=0-521-61719-7\|url=http://books~~.~~google.com/books?id=BZDfFIpCoaAC&dq=Bosonization+and+Strongly+Correlated+Systems&lr=&source=gbs_navlinks_s}}~~<~~/ref~~> The method of bosonization was conceived independently by particle physicists [[Sidney Coleman]] and [[Stanley Mandelstam]]; and condensed matter physicists [[Daniel Mattis]] and [[Alan Luther]] in 1975.<~~ref name=gogolin /~~>		Hello. Let me introduce the writer. Her name is Emilia Shroyer but it's not the most female title out there. To gather cash is a factor that I'm completely addicted to. I am a meter reader but I plan on altering it. California is exactly where I've always been residing and I adore each working day living here.<br><br>Here is my homepage: [http://www.adosphere.com/poyocum std home test]

	~~The basic physical idea behind bosonization~~ is ~~that~~ [[Dirac sea\|particle-hole excitations]] are bosonic in character. However, it was shown by [[Sin-Itiro Tomonaga\|Tomonaga]] in 1950 that this principle is only valid in one-dimensional systems.<ref name=senechal>{{cite journal\|last=Sénéchal\|first=David\|title=An Introduction to Bosonization\|journal=Theoretical Methods for Strongly Correlated Electrons\|year=1999\|series=CRM Series in Mathematical Physics\|doi=10.1007/0-387-21717-7_4\|url=http://www.~~springerlink~~.com/content/q8p7094320733111/}}</ref> Bosonization is an [[effective field theory]] that focuses on low-energy excitations.<ref name=glazman>{{cite book\|last=Sohn\|first=Lydia (ed.)\|title=Mesoscopic electron transport\|year=1997\|publisher=Springer\|isbn=0-7923-4737-4\|url=http://arxiv.org/pdf/cond-mat/9610037v1.pdf}}</ref>

	~~Two complex fermions <math>\psi,\bar\psi</math> are written as functions of a boson <math>\phi</math>~~
	~~:<math>\bar\psi_-\psi_+ = :\exp(i\phi):,\qquad \bar\psi_-\psi_+ = :\exp(-i\phi):</math><ref>~~
	~~In actuality, there is a [[cocycle]] prefactor to give correct (anti-)commutation relations with other fields under consideration.</ref>~~
	~~while the inverse map is given by~~
	~~:<math>\partial\phi=:\bar\psi\psi:</math>~~
	~~All equations are [[normal-order]]ed. The changed statistics arises from [[anomalous dimension]]s of the fields.~~

	~~==References==~~
	~~<references />~~

	~~[[Category:Quantum field theory]]~~
	~~[[Category:Condensed matter physics]~~]

	~~{{quantum-stub}}~~

150.244.37.45: /* Finding wavefunctions for the bound state */ minor edit fixed typo

2013-10-21T16:44:05Z

Finding wavefunctions for the bound state: minor edit fixed typo

← Older revision		Revision as of 18:44, 21 October 2013
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	~~Greetings! I am Marvella and I feel comfy when individuals use the full title. His spouse doesn~~'~~t like it the std home test way he does but what he truly at home std~~ [http://~~glskating~~.com/~~groups~~/~~stay~~-~~yeast~~-~~infection~~-~~free~~-~~with~~-~~these~~-~~helpful-suggestions/ glskating.com] test likes doing is to do [~~http://~~ohnotheydidnt~~.~~livejournal~~.com/~~49721712~~.~~html aerobics] [~~http://~~dateplate~~.~~com~~/~~dayzfe http:~~//~~dateplate~~.~~com~~/~~] and he's been doing it for fairly~~ a ~~while. Years in the past we moved to North Dakota. He used to be unemployed but now he~~ is a ~~meter reader~~.<br><br>~~my webpage~~ :: ~~over at home std test the counter std test~~ - [~~http://theoffshoremanual~~.~~com~~/~~?testimonial=know-facing-candida~~-~~albicans websites],~~		In [[theoretical physics\|theoretical]] [[condensed matter physics]], '''Bosonization''' is a mathematical procedure by which a system of interacting [[fermions]] in [[dimension\|(1+1) dimensions]] can be transformed to a system of massless, non-interacting [[bosons]].<ref name=gogolin>{{cite book\|last=Gogolin\|first=Alexander O.\|title=Bosonization and Strongly Correlated Systems\|year=2004\|publisher=Cambridge University Press\|isbn=0-521-61719-7\|url=http://books.google.com/books?id=BZDfFIpCoaAC&dq=Bosonization+and+Strongly+Correlated+Systems&lr=&source=gbs_navlinks_s}}</ref> The method of bosonization was conceived independently by particle physicists [[Sidney Coleman]] and [[Stanley Mandelstam]]; and condensed matter physicists [[Daniel Mattis]] and [[Alan Luther]] in 1975.<ref name=gogolin />

			The basic physical idea behind bosonization is that [[Dirac sea\|particle-hole excitations]] are bosonic in character. However, it was shown by [[Sin-Itiro Tomonaga\|Tomonaga]] in 1950 that this principle is only valid in one-dimensional systems.<ref name=senechal>{{cite journal\|last=Sénéchal\|first=David\|title=An Introduction to Bosonization\|journal=Theoretical Methods for Strongly Correlated Electrons\|year=1999\|series=CRM Series in Mathematical Physics\|doi=10.1007/0-387-21717-7_4\|url=http://www.springerlink.com/content/q8p7094320733111/}}</ref> Bosonization is an [[effective field theory]] that focuses on low-energy excitations.<ref name=glazman>{{cite book\|last=Sohn\|first=Lydia (ed.)\|title=Mesoscopic electron transport\|year=1997\|publisher=Springer\|isbn=0-7923-4737-4\|url=http://arxiv.org/pdf/cond-mat/9610037v1.pdf}}</ref>

			Two complex fermions <math>\psi,\bar\psi</math> are written as functions of a boson <math>\phi</math>
			:<math>\bar\psi_-\psi_+ = :\exp(i\phi):,\qquad \bar\psi_-\psi_+ = :\exp(-i\phi):</math><ref>
			In actuality, there is a [[cocycle]] prefactor to give correct (anti-)commutation relations with other fields under consideration.</ref>
			while the inverse map is given by
			:<math>\partial\phi=:\bar\psi\psi:</math>
			All equations are [[normal-order]]ed. The changed statistics arises from [[anomalous dimension]]s of the fields.

			==References==
			<references />

			[[Category:Quantum field theory]]
			[[Category:Condensed matter physics]]

			{{quantum-stub}}

74.97.185.246: /* Finding wavefunctions for the bound state */

2012-08-28T19:42:36Z

Finding wavefunctions for the bound state

New page

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