Physics:Quantum defect - Revision history

WikiHarold: Use Quantum See also index module

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	~~==See also==~~
	*External quantum efficiency
	*Quantum efficiency of a solar cell

	== See also ==		== See also ==

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	The '''quantum defect''' of an alkali atom refers to a correction to the energy levels predicted by the classic calculation of the hydrogen wavefunction. A simple model of the potential experienced by the single valence electron of an alkali atom is that the ionic core acts as a point charge with effective charge e and the wavefunctions are hydrogenic. However, the structure of the ionic core alters the potential at small radii.<ref>http://www.phy.davidson.edu/StuHome/joesten/IntLab/final/rydberg.htm, Rydberg Atoms and the Quantum Defect at the site of Davidson College, Physics department</ref>		The '''quantum defect''' of an alkali atom refers to a correction to the energy levels predicted by the classic calculation of the hydrogen wavefunction. A simple model of the potential experienced by the single valence electron of an alkali atom is that the ionic core acts as a point charge with effective charge e and the wavefunctions are hydrogenic. However, the structure of the ionic core alters the potential at small radii.<ref>http://www.phy.davidson.edu/StuHome/joesten/IntLab/final/rydberg.htm, Rydberg Atoms and the Quantum Defect at the site of Davidson College, Physics department</ref>

	The 1/''r'' potential in the [[Physics:~~Hydrogen atom~~\|hydrogen atom]] leads to an electron binding energy given by		The 1/''r'' potential in the [[Physics:Quantum atoms/hydrogen\|hydrogen atom]] leads to an electron binding energy given by
	<math display="block">E_\text{B} = -\dfrac{Rhc}{n^2},</math>		<math display="block">E_\text{B} = -\dfrac{Rhc}{n^2},</math>
	where <math>R</math> is the Rydberg constant, <math>h</math> is Planck's constant, <math>c</math> is the speed of light and <math>n</math> is the principal quantum number.		where <math>R</math> is the Rydberg constant, <math>h</math> is Planck's constant, <math>c</math> is the speed of light and <math>n</math> is the principal quantum number.

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	'''defect''' ~~is a Book I topic in~~ the ~~Quantum Collection. The~~ term quantum defect refers to two concepts: energy loss in lasers and energy levels in alkali elements. Both deal with quantum systems where matter interacts with light. The term quantum defect refers to two concepts: energy loss in lasers and energy levels in alkali elements. Both deal with quantum systems where matter interacts with light. In laser science, the term "quantum defect" refers to the fact that the energy of a pump photon is generally higher than that of a signal photon (photon of the output radiation). The energy difference is lost to heat, which may carry away the excess entropy delivered by the multimode incoherent pump.		'''defect''' the term quantum defect refers to two concepts: energy loss in lasers and energy levels in alkali elements. Both deal with quantum systems where matter interacts with light. The term quantum defect refers to two concepts: energy loss in lasers and energy levels in alkali elements. Both deal with quantum systems where matter interacts with light. In laser science, the term "quantum defect" refers to the fact that the energy of a pump photon is generally higher than that of a signal photon (photon of the output radiation). The energy difference is lost to heat, which may carry away the excess entropy delivered by the multimode incoherent pump.
	</div>		</div>

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	*External quantum efficiency		*External quantum efficiency
	*Quantum efficiency of a solar cell		*Quantum efficiency of a solar cell

			== See also ==
			{{#invoke:PhysicsQC\|tocHeadingAndList\|Physics:Quantum basics/See also}}

	==References==		==References==
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	[[Category:Laser science]]		[[Category:Laser science]]

	{{Sourceattribution\|Quantum defect\|1}}		{{Author\|Harold Foppele}}

			{{Sourceattribution\|Physics:Quantum defect\|1}}

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	~~The term~~ '''~~quantum~~ defect''' refers to two concepts: energy loss in lasers and energy levels in ~~[[Chemistry~~:~~Alkali metal\|~~alkali elements]]. Both deal with ~~[[Physics:Quantum\|~~quantum]] systems where matter interacts with light.		'''defect''' is a Book I topic in the Quantum Collection. The term quantum defect refers to two concepts: energy loss in lasers and energy levels in alkali elements. Both deal with quantum systems where matter interacts with light. The term quantum defect refers to two concepts: energy loss in lasers and energy levels in alkali elements. Both deal with quantum systems where matter interacts with light. In laser science, the term "quantum defect" refers to the fact that the energy of a pump photon is generally higher than that of a signal photon (photon of the output radiation). The energy difference is lost to heat, which may carry away the excess entropy delivered by the multimode incoherent pump.
	</div>		</div>

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	==In laser science==		==In laser science==
	In ~~[[Physics:Laser\|~~laser]] science, the term "'''quantum defect'''" refers to the fact that the energy of a pump photon is generally higher than that of a ''signal photon'' (photon of the output radiation). The energy difference is lost to heat, which may carry away the excess ~~[[Physics:Entropy\|~~entropy]] delivered by the multimode incoherent pump.		In laser science, the term "'''quantum defect'''" refers to the fact that the energy of a pump photon is generally higher than that of a ''signal photon'' (photon of the output radiation). The energy difference is lost to heat, which may carry away the excess entropy delivered by the multimode incoherent pump.

	The quantum defect of a ~~[[Physics:Laser\|~~laser]] can be defined as the part of the energy of the pumping photon which is lost (not turned into photons at the lasing wavelength) in the gain medium during lasing.<ref name="LaserQD">{{cite journal \| author = T.Y.Fan \| title = Heat generation in Nd:YAG and Yb:YAG \| journal = ~~[[Physics:~~IEEE Journal of Quantum Electronics~~\|IEEE Journal of Quantum Electronics]]~~ \| volume = 29 \| issue = 6 \| pages = 1457–1459 \| date = 1993 \| doi = 10.1109/3.234394 \| bibcode = 1993IJQE...29.1457F }}</ref> At given frequency <math>\omega_{\rm p}</math> of ~~[[Engineering:Pump\|~~pump]] and given frequency <math>\omega_{\rm s}</math> of lasing, the quantum defect <math>q = \hbar \omega_{\rm p} - \hbar\omega_{\rm s}</math>. Such a quantum defect has dimensions of energy; for the efficient operation, the ~~[[Physics:Temperature\|~~temperature]] of the gain medium		The quantum defect of a laser can be defined as the part of the energy of the pumping photon which is lost (not turned into photons at the lasing wavelength) in the gain medium during lasing.<ref name="LaserQD">{{cite journal \| author = T.Y.Fan \| title = Heat generation in Nd:YAG and Yb:YAG \| journal = IEEE Journal of Quantum Electronics \| volume = 29 \| issue = 6 \| pages = 1457–1459 \| date = 1993 \| doi = 10.1109/3.234394 \| bibcode = 1993IJQE...29.1457F }}</ref> At given frequency <math>\omega_{\rm p}</math> of pump and given frequency <math>\omega_{\rm s}</math> of lasing, the quantum defect <math>q = \hbar \omega_{\rm p} - \hbar\omega_{\rm s}</math>. Such a quantum defect has dimensions of energy; for the efficient operation, the temperature of the gain medium
	(measured in units of energy) should be small compared to the quantum defect.		(measured in units of energy) should be small compared to the quantum defect.

	The quantum defect may also be defined as follows: at a given frequency <math>\omega_{\rm p}</math> of ~~[[Engineering:Pump\|~~pump]] and given frequency <math>\omega_{\rm s}</math> of lasing, the quantum defect <math>q = 1 - \omega_{\rm s}/\omega_{\rm p}</math>; according to this definition, '''quantum defect''' is dimensionless.{{Citation needed\|date=March 2023}}		The quantum defect may also be defined as follows: at a given frequency <math>\omega_{\rm p}</math> of pump and given frequency <math>\omega_{\rm s}</math> of lasing, the quantum defect <math>q = 1 - \omega_{\rm s}/\omega_{\rm p}</math>; according to this definition, '''quantum defect''' is dimensionless.{{Citation needed\|date=March 2023}}
	At a fixed pump frequency, the higher the quantum defect, the lower is the upper bound for the power efficiency.		At a fixed pump frequency, the higher the quantum defect, the lower is the upper bound for the power efficiency.

	==In hydrogenic atoms==		==In hydrogenic atoms==

	[[File:Atom-sodium.png\|thumb\|In an idealized ~~[[Physics:~~Bohr model~~\|Bohr model]]~~ alkali atom (such as sodium, pictured here), the single outer-shell electron stays outside the ionic core and it would be expected to behave just as if in the same orbital of a hydrogen atom.]]		[[File:Atom-sodium.png\|thumb\|In an idealized Bohr model alkali atom (such as sodium, pictured here), the single outer-shell electron stays outside the ionic core and it would be expected to behave just as if in the same orbital of a hydrogen atom.]]

	The '''quantum defect''' of an ~~[[Chemistry:Alkali metal\|~~alkali atom]] refers to a correction to the energy levels predicted by the classic calculation of the hydrogen wavefunction. A simple model of the potential experienced by the single valence electron of an alkali atom is that the ionic core acts as a point charge with effective charge ~~[[Physics:Elementary charge\|~~e]] and the wavefunctions are ~~[[Physics:Hydrogen-like atom\|~~hydrogenic]]. However, the structure of the ionic core alters the potential at small radii.<ref>http://www.phy.davidson.edu/StuHome/joesten/IntLab/final/rydberg.htm, Rydberg Atoms and the Quantum Defect at the site of ~~[[Organization:Davidson College\|~~Davidson College]], Physics department</ref>		The '''quantum defect''' of an alkali atom refers to a correction to the energy levels predicted by the classic calculation of the hydrogen wavefunction. A simple model of the potential experienced by the single valence electron of an alkali atom is that the ionic core acts as a point charge with effective charge e and the wavefunctions are hydrogenic. However, the structure of the ionic core alters the potential at small radii.<ref>http://www.phy.davidson.edu/StuHome/joesten/IntLab/final/rydberg.htm, Rydberg Atoms and the Quantum Defect at the site of Davidson College, Physics department</ref>

	The 1/''r'' potential in the [[Physics:Hydrogen atom\|hydrogen atom]] leads to an ~~[[Physics:Electron\|~~electron~~]] [[Physics:Binding energy\|~~binding energy]] given by		The 1/''r'' potential in the [[Physics:Hydrogen atom\|hydrogen atom]] leads to an electron binding energy given by
	<math display="block">E_\text{B} = -\dfrac{Rhc}{n^2},</math>		<math display="block">E_\text{B} = -\dfrac{Rhc}{n^2},</math>
	where <math>R</math> is the ~~[[Physics:~~Rydberg constant~~\|Rydberg constant]]~~, <math>h</math> is Planck's constant, <math>c</math> is the ~~[[Physics:Speed of light\|~~speed of light]] and <math>n</math> is the ~~[[Physics:Principal quantum number\|~~principal quantum number]].		where <math>R</math> is the Rydberg constant, <math>h</math> is Planck's constant, <math>c</math> is the speed of light and <math>n</math> is the principal quantum number.

	For ~~[[Chemistry:Alkali metal\|~~alkali atoms]] with small ~~[[Physics:Angular momentum operator\|~~orbital angular momentum]], the wavefunction of the valence electron is non-negligible in the ion core where the screened Coulomb potential with an effective charge of ~~[[Physics:Elementary charge\|~~e]] no longer describes the potential. The spectrum is still described well by the ~~[[Physics:Rydberg formula\|~~Rydberg formula]] with an angular momentum dependent quantum defect, <math>\delta_l</math>:		For alkali atoms with small orbital angular momentum, the wavefunction of the valence electron is non-negligible in the ion core where the screened Coulomb potential with an effective charge of e no longer describes the potential. The spectrum is still described well by the Rydberg formula with an angular momentum dependent quantum defect, <math>\delta_l</math>:
	<math display="block">E_\text{B} = -\dfrac{Rhc}{(n-\delta_l)^2}.</math>		<math display="block">E_\text{B} = -\dfrac{Rhc}{(n-\delta_l)^2}.</math>