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en>BG19bot: WP:CHECKWIKI error fix for #61. Punctuation goes before References. Do general fixes if a problem exists. - using AWB (9916)

2014-02-07T08:40:53Z

WP:CHECKWIKI error fix for #61. Punctuation goes before References. Do general fixes if a problem exists. - using AWB (9916)

← Older revision		Revision as of 10:40, 7 February 2014
Line 1:		Line 1:
	~~The '''Kramers-Heisenberg dispersion formula'''~~ is ~~an expression for the [[cross section (physics)\|cross section]] for [[scattering]] of a [[photon]]~~ by ~~an [[atom]]ic [[electron]]. It was derived before~~ the ~~advent~~ of ~~[[quantum mechanics]] by [[Hendrik Anthony Kramers\|Hendrik Kramers]] and [[Werner Heisenberg]] in 1925,<ref name=KH>{{cite journal~~		She is recognized by the title of Myrtle Shryock. For years he's been operating as a receptionist. To gather coins is what his family and him appreciate. California is our beginning place.<br><br>Here is my website - at home std test ([http://dtekorea.com/xe/DS_030111/1073195 visit the next internet site])
	~~\| last = Kramers~~
	~~\| first = H~~. A.
	~~\| authorlink = Hendrik Anthony Kramers~~
	~~\| last2 = Heisenberg~~
	~~\| first2 = W.~~
	~~\| author2-link = Werner Heisenberg~~
	~~\| title = Über die Streuung von Strahlung durch Atome~~
	~~\| journal = Z. Phys.~~
	~~\| volume = 31~~
	~~\| issue = 1~~
	~~\| pages = 681–708~~
	~~\| date = Feb 1925~~
	~~\| url = http://www.springerlink.com/content/x2x7220805540747~~
	~~\| doi = 10.1007/BF02980624~~
	\|bibcode = 1925ZPhy...31..681K }}</ref> based on the [[correspondence principle]] applied to the classical dispersion formula for light. The quantum mechanical derivation was given by [[Paul Dirac]] in 1927.<ref>{{cite journal
	~~\| last = Dirac.~~
	~~\| first = P. A. M.~~
	~~\| authorlink = Paul Dirac~~
	~~\| title = The Quantum Theory of the Emission~~ and ~~Absorption of Radiation~~
	~~\| journal = Proc~~. ~~Roy~~. ~~Soc. Lond. A~~
	~~\| volume = 114~~
	~~\| issue = 769~~
	~~\| pages = 243–265~~
	~~\| year = 1927~~
	~~\| doi = 10.1098/rspa.1927.0039~~
	~~\|bibcode = 1927RSPSA.114..243D }}~~<~~/ref~~><~~ref~~>~~{{cite journal~~
	~~\| last = Dirac.~~
	~~\| first = P. A. M.~~
	~~\| authorlink = Paul Dirac~~
	~~\| title = The Quantum Theory of Dispersion~~
	~~\| journal = Proc. Roy. Soc. Lond. A~~
	~~\| volume = 114~~
	~~\| issue = 769~~
	~~\| pages = 710–728~~
	~~\| year = 1927~~
	~~\| doi = 10.1098/rspa.1927.0071~~
	~~\|bibcode = 1927RSPSA.114..710D }}</ref>~~

	~~The Kramers–Heisenberg formula was an important achievement when it was published, explaining the notion of "negative absorption"~~ ([[stimulated emission]]), the Thomas-Reiche-Kuhn sum rule, and [[inelastic scattering]] - where the [[energy]] of the scattered photon may be larger or smaller than that of the incident photon - thereby anticipating the [[Raman effect]].<ref>{{Cite journal
	~~\| last = Breit~~
	~~\| first = G.~~
	~~\| title = Quantum Theory of Dispersion~~
	~~\| journal = Rev. Mod. Phys.~~
	~~\| volume = 4~~
	~~\| issue = 3~~
	~~\| pages = 504–576~~
	~~\| year = 1932~~
	~~\| url =~~ http://~~link~~.~~aps.org/doi/10.1103/RevModPhys.4.504~~
	~~\| doi = 10.1103/RevModPhys.4.504~~
	~~\|bibcode = 1932RvMP....4..504B }}</ref>~~

	~~== Equation ==~~
	~~The Kramers-Heisenberg (KH) formula for second order processes is <ref name=KH~~/~~><ref>J.J. Sakurai, Advanced Quantum Mechanics, Addison-Wesley (1967), page~~
	~~56.<~~/~~ref><BR>~~
	<math> \frac{d^2 \sigma}{d\Omega_{k^\prime}d(\hbar \omega_k^\prime)}=\frac{\omega_k^\prime}{\omega_k}\sum_{\|f\rangle}\left \| \sum_{\|n\rangle} \frac{\langle f \| T^\dagger \| n \rangle \langle n \| T \| i \rangle}{E_i - E_n + \hbar \omega_k + i \frac{\Gamma_n}{2}}\right \|^2 \delta (E_i - E_f + \hbar \omega_k - \hbar \omega_k^\prime)</~~math>~~

	~~It represents~~ the ~~probability of the emission of photons of energy <math> \hbar \omega_k^\prime </math> in the~~
	~~solid angle <math>d\Omega_{k^\prime}</math> (centred in the <math>k^\prime</math> direction~~)~~, after the excitation of the system with photons of energy <math> \hbar \omega_k</math>. <math>\|i\rangle, \|n\rangle, \|f\rangle</math> are the initial, intermediate~~
	~~and ﬁnal states of the system with energy <math>E_i , E_n , E_f</math> respectively; the delta~~
	~~function ensures the energy conservation during the whole process. <math>T</math> is the relevant~~
	~~transition operator. <math>\Gamma_n </math> is the instrinsic linewidth of the intermediate state.~~

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

	~~{{DEFAULTSORT:Kramers-Heisenberg formula}}~~
	~~[[Category:Particle physics]]~~


	~~{{physics-stub}}~~

en>Zanglazor: /* Types */

2014-01-29T17:01:54Z

Types

← Older revision		Revision as of 19:01, 29 January 2014
Line 1:		Line 1:
	The ~~title~~ of the ~~writer is Numbers~~. ~~Playing baseball is~~ the ~~pastime he will~~ by ~~no means quit doing~~. ~~Minnesota is where he's been residing for many years~~. ~~For many years he's been working as a receptionist~~.<br><br>~~Also visit my blog: std home test~~ ([http://~~ironptstudio~~.~~com~~/~~rev~~/~~239375 visit this website link~~])		The '''Kramers-Heisenberg dispersion formula''' is an expression for the [[cross section (physics)\|cross section]] for [[scattering]] of a [[photon]] by an [[atom]]ic [[electron]]. It was derived before the advent of [[quantum mechanics]] by [[Hendrik Anthony Kramers\|Hendrik Kramers]] and [[Werner Heisenberg]] in 1925,<ref name=KH>{{cite journal
			\| last = Kramers
			\| first = H. A.
			\| authorlink = Hendrik Anthony Kramers
			\| last2 = Heisenberg
			\| first2 = W.
			\| author2-link = Werner Heisenberg
			\| title = Über die Streuung von Strahlung durch Atome
			\| journal = Z. Phys.
			\| volume = 31
			\| issue = 1
			\| pages = 681–708
			\| date = Feb 1925
			\| url = http://www.springerlink.com/content/x2x7220805540747
			\| doi = 10.1007/BF02980624
			\|bibcode = 1925ZPhy...31..681K }}</ref> based on the [[correspondence principle]] applied to the classical dispersion formula for light. The quantum mechanical derivation was given by [[Paul Dirac]] in 1927.<ref>{{cite journal
			\| last = Dirac.
			\| first = P. A. M.
			\| authorlink = Paul Dirac
			\| title = The Quantum Theory of the Emission and Absorption of Radiation
			\| journal = Proc. Roy. Soc. Lond. A
			\| volume = 114
			\| issue = 769
			\| pages = 243–265
			\| year = 1927
			\| doi = 10.1098/rspa.1927.0039
			\|bibcode = 1927RSPSA.114..243D }}</ref><ref>{{cite journal
			\| last = Dirac.
			\| first = P. A. M.
			\| authorlink = Paul Dirac
			\| title = The Quantum Theory of Dispersion
			\| journal = Proc. Roy. Soc. Lond. A
			\| volume = 114
			\| issue = 769
			\| pages = 710–728
			\| year = 1927
			\| doi = 10.1098/rspa.1927.0071
			\|bibcode = 1927RSPSA.114..710D }}</ref>

			The Kramers–Heisenberg formula was an important achievement when it was published, explaining the notion of "negative absorption" ([[stimulated emission]]), the Thomas-Reiche-Kuhn sum rule, and [[inelastic scattering]] - where the [[energy]] of the scattered photon may be larger or smaller than that of the incident photon - thereby anticipating the [[Raman effect]].<ref>{{Cite journal
			\| last = Breit
			\| first = G.
			\| title = Quantum Theory of Dispersion
			\| journal = Rev. Mod. Phys.
			\| volume = 4
			\| issue = 3
			\| pages = 504–576
			\| year = 1932
			\| url = http://link.aps.org/doi/10.1103/RevModPhys.4.504
			\| doi = 10.1103/RevModPhys.4.504
			\|bibcode = 1932RvMP....4..504B }}</ref>

			== Equation ==
			The Kramers-Heisenberg (KH) formula for second order processes is <ref name=KH/><ref>J.J. Sakurai, Advanced Quantum Mechanics, Addison-Wesley (1967), page
			56.</ref><BR>
			<math> \frac{d^2 \sigma}{d\Omega_{k^\prime}d(\hbar \omega_k^\prime)}=\frac{\omega_k^\prime}{\omega_k}\sum_{\|f\rangle}\left \| \sum_{\|n\rangle} \frac{\langle f \| T^\dagger \| n \rangle \langle n \| T \| i \rangle}{E_i - E_n + \hbar \omega_k + i \frac{\Gamma_n}{2}}\right \|^2 \delta (E_i - E_f + \hbar \omega_k - \hbar \omega_k^\prime)</math>

			It represents the probability of the emission of photons of energy <math> \hbar \omega_k^\prime </math> in the
			solid angle <math>d\Omega_{k^\prime}</math> (centred in the <math>k^\prime</math> direction), after the excitation of the system with photons of energy <math> \hbar \omega_k</math>. <math>\|i\rangle, \|n\rangle, \|f\rangle</math> are the initial, intermediate
			and ﬁnal states of the system with energy <math>E_i , E_n , E_f</math> respectively; the delta
			function ensures the energy conservation during the whole process. <math>T</math> is the relevant
			transition operator. <math>\Gamma_n </math> is the instrinsic linewidth of the intermediate state.

			== References ==
			<references />

			{{DEFAULTSORT:Kramers-Heisenberg formula}}
			[[Category:Particle physics]]


			{{physics-stub}}

62.145.19.66 at 16:28, 25 July 2012

2012-07-25T16:28:24Z

New page

The title of the writer is Numbers. Playing baseball is the pastime he will by no means quit doing. Minnesota is where he's been residing for many years. For many years he's been working as a receptionist.<br><br>Also visit my blog: std home test ([http://ironptstudio.com/rev/239375 visit this website link])

← Older revision		Revision as of 10:40, 7 February 2014
Line 1:		Line 1:
	~~The '''Kramers-Heisenberg dispersion formula'''~~ is ~~an expression for the [[cross section (physics)\|cross section]] for [[scattering]] of a [[photon]]~~ by ~~an [[atom]]ic [[electron]]. It was derived before~~ the ~~advent~~ of ~~[[quantum mechanics]] by [[Hendrik Anthony Kramers\|Hendrik Kramers]] and [[Werner Heisenberg]] in 1925,<ref name=KH>{{cite journal~~		She is recognized by the title of Myrtle Shryock. For years he's been operating as a receptionist. To gather coins is what his family and him appreciate. California is our beginning place.<br><br>Here is my website - at home std test ([http://dtekorea.com/xe/DS_030111/1073195 visit the next internet site])
	~~\| last = Kramers~~
	~~\| first = H~~. A.
	~~\| authorlink = Hendrik Anthony Kramers~~
	~~\| last2 = Heisenberg~~
	~~\| first2 = W.~~
	~~\| author2-link = Werner Heisenberg~~
	~~\| title = Über die Streuung von Strahlung durch Atome~~
	~~\| journal = Z. Phys.~~
	~~\| volume = 31~~
	~~\| issue = 1~~
	~~\| pages = 681–708~~
	~~\| date = Feb 1925~~
	~~\| url = http://www.springerlink.com/content/x2x7220805540747~~
	~~\| doi = 10.1007/BF02980624~~
	\|bibcode = 1925ZPhy...31..681K }}</ref> based on the [[correspondence principle]] applied to the classical dispersion formula for light. The quantum mechanical derivation was given by [[Paul Dirac]] in 1927.<ref>{{cite journal
	~~\| last = Dirac.~~
	~~\| first = P. A. M.~~
	~~\| authorlink = Paul Dirac~~
	~~\| title = The Quantum Theory of the Emission~~ and ~~Absorption of Radiation~~
	~~\| journal = Proc~~. ~~Roy~~. ~~Soc. Lond. A~~
	~~\| volume = 114~~
	~~\| issue = 769~~
	~~\| pages = 243–265~~
	~~\| year = 1927~~
	~~\| doi = 10.1098/rspa.1927.0039~~
	~~\|bibcode = 1927RSPSA.114..243D }}~~<~~/ref~~><~~ref~~>~~{{cite journal~~
	~~\| last = Dirac.~~
	~~\| first = P. A. M.~~
	~~\| authorlink = Paul Dirac~~
	~~\| title = The Quantum Theory of Dispersion~~
	~~\| journal = Proc. Roy. Soc. Lond. A~~
	~~\| volume = 114~~
	~~\| issue = 769~~
	~~\| pages = 710–728~~
	~~\| year = 1927~~
	~~\| doi = 10.1098/rspa.1927.0071~~
	~~\|bibcode = 1927RSPSA.114..710D }}</ref>~~

	~~The Kramers–Heisenberg formula was an important achievement when it was published, explaining the notion of "negative absorption"~~ ([[stimulated emission]]), the Thomas-Reiche-Kuhn sum rule, and [[inelastic scattering]] - where the [[energy]] of the scattered photon may be larger or smaller than that of the incident photon - thereby anticipating the [[Raman effect]].<ref>{{Cite journal
	~~\| last = Breit~~
	~~\| first = G.~~
	~~\| title = Quantum Theory of Dispersion~~
	~~\| journal = Rev. Mod. Phys.~~
	~~\| volume = 4~~
	~~\| issue = 3~~
	~~\| pages = 504–576~~
	~~\| year = 1932~~
	~~\| url =~~ http://~~link~~.~~aps.org/doi/10.1103/RevModPhys.4.504~~
	~~\| doi = 10.1103/RevModPhys.4.504~~
	~~\|bibcode = 1932RvMP....4..504B }}</ref>~~

	~~== Equation ==~~
	~~The Kramers-Heisenberg (KH) formula for second order processes is <ref name=KH~~/~~><ref>J.J. Sakurai, Advanced Quantum Mechanics, Addison-Wesley (1967), page~~
	~~56.<~~/~~ref><BR>~~
	<math> \frac{d^2 \sigma}{d\Omega_{k^\prime}d(\hbar \omega_k^\prime)}=\frac{\omega_k^\prime}{\omega_k}\sum_{\|f\rangle}\left \| \sum_{\|n\rangle} \frac{\langle f \| T^\dagger \| n \rangle \langle n \| T \| i \rangle}{E_i - E_n + \hbar \omega_k + i \frac{\Gamma_n}{2}}\right \|^2 \delta (E_i - E_f + \hbar \omega_k - \hbar \omega_k^\prime)</~~math>~~

	~~It represents~~ the ~~probability of the emission of photons of energy <math> \hbar \omega_k^\prime </math> in the~~
	~~solid angle <math>d\Omega_{k^\prime}</math> (centred in the <math>k^\prime</math> direction~~)~~, after the excitation of the system with photons of energy <math> \hbar \omega_k</math>. <math>\|i\rangle, \|n\rangle, \|f\rangle</math> are the initial, intermediate~~
	~~and ﬁnal states of the system with energy <math>E_i , E_n , E_f</math> respectively; the delta~~
	~~function ensures the energy conservation during the whole process. <math>T</math> is the relevant~~
	~~transition operator. <math>\Gamma_n </math> is the instrinsic linewidth of the intermediate state.~~

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

	~~{{DEFAULTSORT:Kramers-Heisenberg formula}}~~
	~~[[Category:Particle physics]]~~


	~~{{physics-stub}}~~