Physics:Quantum Stark effect - Revision history

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	The Stark effect is used to slow down and manipulate molecular beams.<ref>{{Cite journal \|last=van de Meerakker \|first=Sebastiaan Y. T. \|last2=Bethlem \|first2=Hendrick L. \|last3=Vanhaecke \|first3=Nicolas \|last4=Meijer \|first4=Gerard \|date=2012-09-12 \|title=Manipulation and Control of Molecular Beams \|url=https://doi.org/10.1021/cr200349r \|journal=Chemical Reviews \|volume=112 \|issue=9 \|pages=4828–4878 \|doi=10.1021/cr200349r \|issn=0009-2665}}</ref>		The Stark effect is used to slow down and manipulate molecular beams.<ref>{{Cite journal \|last=van de Meerakker \|first=Sebastiaan Y. T. \|last2=Bethlem \|first2=Hendrick L. \|last3=Vanhaecke \|first3=Nicolas \|last4=Meijer \|first4=Gerard \|date=2012-09-12 \|title=Manipulation and Control of Molecular Beams \|url=https://doi.org/10.1021/cr200349r \|journal=Chemical Reviews \|volume=112 \|issue=9 \|pages=4828–4878 \|doi=10.1021/cr200349r \|issn=0009-2665}}</ref>

	==See also==		== See also ==
	*Zeeman effect		{{#invoke:PhysicsQC\|tocHeadingAndList\|Physics:Quantum basics/See also}}
	*Autler–Townes effect
	*[[Physics:Quantum~~-confined Stark effect\|Quantum-confined Stark effect]]~~
	*Stark spectroscopy
	*Inglis–Teller equation
	*Electric field NMR
	*Stark effect in semiconductor optics

	==Further reading==		==Further reading==
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	* {{cite book \| author=H. Friedrich\|title=Theoretical Atomic Physics\| url=https://archive.org/details/theoreticalatomi0000frie\| url-access=registration\| publisher=Springer-Verlag, Berlin \|date=1990 \|isbn=978-0-387-54179-2 }} ''(Stark effect for atoms)''		* {{cite book \| author=H. Friedrich\|title=Theoretical Atomic Physics\| url=https://archive.org/details/theoreticalatomi0000frie\| url-access=registration\| publisher=Springer-Verlag, Berlin \|date=1990 \|isbn=978-0-387-54179-2 }} ''(Stark effect for atoms)''
	* {{cite book \| author=H. W. Kroto\|title=Molecular Rotation Spectra\| publisher=Dover, New York \|date=1992 \|isbn=978-0-486-67259-5 }} ''(Stark effect for rotating molecules)''		* {{cite book \| author=H. W. Kroto\|title=Molecular Rotation Spectra\| publisher=Dover, New York \|date=1992 \|isbn=978-0-486-67259-5 }} ''(Stark effect for rotating molecules)''

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

	== References ==		== References ==

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	<div style="flex:1; line-height:1.45; color:#006b45; column-count:2; column-gap:32px; column-rule:1px solid #b8d8c8;">		<div style="flex:1; line-height:1.45; color:#006b45; column-count:2; column-gap:32px; column-rule:1px solid #b8d8c8;">
	~~The~~ '''Stark effect''' is the shifting and splitting of spectral lines of atoms and molecules due to the presence of an external electric field. It is the electric-field analogue of the Zeeman effect, where a spectral line is split into several components due to the presence of the magnetic field. Although initially coined for the static case, it is also used in the wider context to describe the effect of time-dependent electric fields. In particular, the Stark effect is responsible for the pressure broadening (Stark broadening) of spectral lines by charged particles in plasmas. For most spectral lines, the Stark effect is either linear (proportional to the applied electric field) or quadratic with a high accuracy.		'''Stark effect''' the Stark effect is the shifting and splitting of spectral lines of atoms and molecules due to the presence of an external electric field. It is the electric-field analogue of the Zeeman effect, where a spectral line is split into several components due to the presence of the magnetic field. Although initially coined for the static case, it is also used in the wider context to describe the effect of time-dependent electric fields. In particular, the Stark effect is responsible for the pressure broadening (Stark broadening) of spectral lines by charged particles in plasmas. For most spectral lines, the Stark effect is either linear (proportional to the applied electric field) or quadratic with a high accuracy. The Stark effect can be observed both for emission and absorption lines. The latter was sometimes called the inverse Stark effect, but this term is no longer used in the modern literature. Each n level consists of n degenerate sublevels; application of an electric field breaks the degeneracy. Note how a complicated pattern of the energy levels emerges as the electric field increases, not unlike bifurcations of closed orbits in classical dynamical systems leading to chaos. The effect is named after the German physicist Johannes Stark, who discovered it in 1913.

	The Stark effect can be observed both for emission and absorption lines. The latter was sometimes called the ~~'''~~inverse Stark effect~~'''~~, but this term is no longer used in the modern literature.

	~~<div style="float:right; border:1px solid #ccc; padding:4px; background:#ffffe0; margin:0 0 1em 1em; width:250px; text-align:center;">~~

	~~'''[https://freetocopy.co.nl/Quantum/Animations%20of%20atomic%20physics/stark.gif ▶ Play movie]~~
	~~<div style="font-size:90%; margin-top:4px;">~~
	~~Computed energy level spectrum of hydrogen as a function of the electric field near ''n'' = 15 for magnetic quantum number ''m'' = 0.~~ Each ''n'' level consists of ''n'' degenerate sublevels; application of an electric field breaks the degeneracy~~. Energy levels can cross due to underlying symmetries of motion in the Coulomb potential.]]~~
	~~</div>~~
	~~</div>~~
	~~-level spectrum as a function of the electric field near ''n'' = 15 for ''m'' = 0~~. Note how a complicated pattern of the energy levels emerges as the electric field increases, not unlike
	bifurcations of closed orbits in classical dynamical systems leading to chaos. ~~<ref name=Courtney1995>{{cite journal \|last=Courtney \|first=Michael \|author2=Neal Spellmeyer \|author3=Hong Jiao \|author4=Daniel Kleppner \|title=Classical~~, ~~semiclassical, and quantum dynamics of lithium~~ in ~~an electric field \|journal=Physical Review A \|date=1995 \|volume=51 \|issue=5 \|pages=3604–3620 \|doi=10.1103/PhysRevA.51.3604\|bibcode = 1995PhRvA..51~~.~~3604C \|pmid=9912027}}</ref>]]~~
	</div>		</div>

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	'''[https://freetocopy.co.nl/Quantum/Animations%20of%20atomic%20physics/stark.gif ▶ Play movie]		'''[https://freetocopy.co.nl/Quantum/Animations%20of%20atomic%20physics/stark.gif ▶ Play movie]
	<div style="font-size:90%; margin-top:4px;">		<div style="font-size:90%; margin-top:4px;">
	Computed energy level spectrum of hydrogen as a function of the electric field near ''n'' = 15 for [[magnetic quantum number]] ''m'' = 0. Each ''n'' level consists of ''n'' degenerate sublevels; application of an electric field breaks the degeneracy. Energy levels can cross due to underlying symmetries of motion in the Coulomb potential.]]		Computed energy level spectrum of hydrogen as a function of the electric field near ''n'' = 15 for magnetic quantum number ''m'' = 0. Each ''n'' level consists of ''n'' degenerate sublevels; application of an electric field breaks the degeneracy. Energy levels can cross due to underlying symmetries of motion in the Coulomb potential.]]
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	===Multipole expansion===		===Multipole expansion===
	~~{{Main article\|~~Multipole expansion}}		''Related topic:'' Multipole expansion

	The Stark effect originates from the interaction between a charge distribution (atom or molecule) and an external electric field.		The Stark effect originates from the interaction between a charge distribution (atom or molecule) and an external electric field.

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	The '''Stark effect''' is the shifting and splitting of spectral lines of atoms and molecules due to the presence of an external electric field. It is the electric-field analogue of the Zeeman effect, where a spectral line is split into several components due to the presence of the magnetic field. Although initially coined for the static case, it is also used in the wider context to describe the effect of time-dependent electric fields. In particular, the Stark effect is responsible for the ~~[[Spectral line#Pressure broadening\|~~pressure broadening]] (Stark broadening) of spectral lines by charged particles in plasmas. For most spectral lines, the Stark effect is either linear (proportional to the applied electric field) or quadratic with a high accuracy.		The '''Stark effect''' is the shifting and splitting of spectral lines of atoms and molecules due to the presence of an external electric field. It is the electric-field analogue of the Zeeman effect, where a spectral line is split into several components due to the presence of the magnetic field. Although initially coined for the static case, it is also used in the wider context to describe the effect of time-dependent electric fields. In particular, the Stark effect is responsible for the pressure broadening (Stark broadening) of spectral lines by charged particles in plasmas. For most spectral lines, the Stark effect is either linear (proportional to the applied electric field) or quadratic with a high accuracy.

	The Stark effect can be observed both for emission and absorption lines. The latter was sometimes called the '''inverse Stark effect''', but this term is no longer used in the modern literature.		The Stark effect can be observed both for emission and absorption lines. The latter was sometimes called the '''inverse Stark effect''', but this term is no longer used in the modern literature.
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	The Stark effect originates from the interaction between a charge distribution (atom or molecule) and an external electric field.		The Stark effect originates from the interaction between a charge distribution (atom or molecule) and an external electric field.
	The interaction energy <math>V_\mathrm{int}</math> of a continuous charge distribution <math>\rho(\mathbf{r})</math>, confined within a finite volume <math>\mathcal{V}</math>, with an external ~~[[Physics:Electrostatic#Electrostatic potential\|~~electrostatic potential]] <math>\phi(\mathbf{r})</math> is		The interaction energy <math>V_\mathrm{int}</math> of a continuous charge distribution <math>\rho(\mathbf{r})</math>, confined within a finite volume <math>\mathcal{V}</math>, with an external electrostatic potential <math>\phi(\mathbf{r})</math> is
	<math display="block"> V_\mathrm{int} = \int\limits_\mathcal{V} \phi(\mathbf{r}) \rho(\mathbf{r}) \;\mathrm{d}^3\mathbf r</math>		<math display="block"> V_\mathrm{int} = \int\limits_\mathcal{V} \phi(\mathbf{r}) \rho(\mathbf{r}) \;\mathrm{d}^3\mathbf r</math>
	This expression is valid classically and quantum-mechanically alike.		This expression is valid classically and quantum-mechanically alike.
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	The one-electron states with even <math>\ell</math> are even under parity, while those with odd <math>\ell</math> are odd under parity. Hence hydrogen-like atoms with ''n''>1 show first-order Stark effect.		The one-electron states with even <math>\ell</math> are even under parity, while those with odd <math>\ell</math> are odd under parity. Hence hydrogen-like atoms with ''n''>1 show first-order Stark effect.

	The first-order Stark effect occurs in rotational transitions of ~~[[Physics:Rotational spectroscopy#Classification of molecular rotors\|~~symmetric top molecules]] (but not for linear and asymmetric molecules). In first approximation a molecule may be seen as a rigid rotor. A symmetric top rigid rotor has the unperturbed eigenstates		The first-order Stark effect occurs in rotational transitions of symmetric top molecules (but not for linear and asymmetric molecules). In first approximation a molecule may be seen as a rigid rotor. A symmetric top rigid rotor has the unperturbed eigenstates
	<math display="block">\|JKM \rangle = (D^J_{MK})^* \quad\text{with}\quad M,K= -J,-J+1,\dots,J</math>		<math display="block">\|JKM \rangle = (D^J_{MK})^* \quad\text{with}\quad M,K= -J,-J+1,\dots,J</math>
	with 2(2''J''+1)-fold degenerate energy for \|K\| > 0 and (2''J''+1)-fold degenerate energy for K=0.		with 2(2''J''+1)-fold degenerate energy for \|K\| > 0 and (2''J''+1)-fold degenerate energy for K=0.
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	*Inglis–Teller equation		*Inglis–Teller equation
	*Electric field NMR		*Electric field NMR
	*~~[[Physics:Coherent effects in semiconductor optics#The excitonic optical Stark effect\|~~Stark effect in semiconductor optics]]		*Stark effect in semiconductor optics

	==Further reading==		==Further reading==

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