Physics:Quantum Aharonov-Bohm effect - Revision history

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	{{Short description\|Quantum phase effect caused by electromagnetic potentials}}		{{Short description\|Quantum phase effect caused by electromagnetic potentials}}
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	{{Quantum article nav\|previous=Physics:Quantum Berry phase\|previous label=Berry phase\|next=Physics:Quantum Scattering theory\|next label=Scattering theory}}		{{Quantum article nav\|previous=Physics:Quantum Berry phase\|previous label=Berry phase\|next=Physics:Quantum Scattering theory\|next label=Scattering theory}}
			\|image=[[File:Quantum_aharonov_bohm_effect_yellow.png\|430px\|Aharonov-Bohm phase shift around a shielded magnetic flux.]]
	[[File:Quantum_aharonov_bohm_effect_yellow.png\|~~thumb\|right\|320px~~\|Aharonov-Bohm phase shift around a shielded magnetic flux.]]		\|text=The '''Quantum Aharonov-Bohm effect''' is a quantum phenomenon in which charged particles are affected by electromagnetic potentials even in regions where the classical electric and magnetic fields vanish. It demonstrates that potentials can have direct physical significance in [[Physics:Quantum mechanics\|quantum mechanics]].<ref>{{cite web \|url=https://en.wikipedia.org/wiki/Aharonov%E2%80%93Bohm_effect \|title=Aharonov-Bohm effect \|publisher=Wikipedia \|access-date=20 May 2026}}</ref>

	The '''Quantum Aharonov-Bohm effect''' is a quantum phenomenon in which charged particles are affected by electromagnetic potentials even in regions where the classical electric and magnetic fields vanish. It demonstrates that potentials can have direct physical significance in [[Physics:Quantum mechanics\|quantum mechanics]].<ref>{{cite web \|url=https://en.wikipedia.org/wiki/Aharonov%E2%80%93Bohm_effect \|title=Aharonov-Bohm effect \|publisher=Wikipedia \|access-date=20 May 2026}}</ref>

	In the magnetic version, an electron wave is split into two paths around a confined magnetic flux. The electrons travel through field-free regions, but the vector potential changes their relative phase. When the paths recombine, the interference pattern shifts according to the enclosed magnetic flux.		In the magnetic version, an electron wave is split into two paths around a confined magnetic flux. The electrons travel through field-free regions, but the vector potential changes their relative phase. When the paths recombine, the interference pattern shifts according to the enclosed magnetic flux.
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	== Phase and potentials ==		== Phase and potentials ==

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	{{Quantum article nav\|previous=Physics:Quantum Berry phase\|previous label=Berry phase\|next=Physics:Quantum Scattering theory\|next label=Scattering theory}}		{{Quantum article nav\|previous=Physics:Quantum Berry phase\|previous label=Berry phase\|next=Physics:Quantum Scattering theory\|next label=Scattering theory}}

	~~<div style="display~~:~~flex; gap:24px; align~~-~~items:flex-start; max-width:1280px; clear:both;">~~		[[File:Quantum_aharonov_bohm_effect_yellow.png\|thumb\|right\|320px\|Aharonov-Bohm phase shift around a shielded magnetic flux.]]
	~~<div style="flex:1 1 680px; min-width:0; line-height:1.55;">~~
	The '''Quantum Aharonov-Bohm effect''' is a quantum phenomenon in which charged particles are affected by electromagnetic potentials even in regions where the classical electric and magnetic fields vanish. It demonstrates that potentials can have direct physical significance in [[Physics:Quantum mechanics\|quantum mechanics]].<ref>{{cite web \|url=https://en.wikipedia.org/wiki/Aharonov%E2%80%93Bohm_effect \|title=Aharonov-Bohm effect \|publisher=Wikipedia \|access-date=20 May 2026}}</ref>		The '''Quantum Aharonov-Bohm effect''' is a quantum phenomenon in which charged particles are affected by electromagnetic potentials even in regions where the classical electric and magnetic fields vanish. It demonstrates that potentials can have direct physical significance in [[Physics:Quantum mechanics\|quantum mechanics]].<ref>{{cite web \|url=https://en.wikipedia.org/wiki/Aharonov%E2%80%93Bohm_effect \|title=Aharonov-Bohm effect \|publisher=Wikipedia \|access-date=20 May 2026}}</ref>

	In the magnetic version, an electron wave is split into two paths around a confined magnetic flux. The electrons travel through field-free regions, but the vector potential changes their relative phase. When the paths recombine, the interference pattern shifts according to the enclosed magnetic flux.		In the magnetic version, an electron wave is split into two paths around a confined magnetic flux. The electrons travel through field-free regions, but the vector potential changes their relative phase. When the paths recombine, the interference pattern shifts according to the enclosed magnetic flux.
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	~~[[File:Quantum_aharonov_bohm_effect_yellow.png\|thumb\|360px\|Aharonov-Bohm phase shift around a shielded magnetic flux.]]~~
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	== Phase and potentials ==		== Phase and potentials ==

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	{{Short description\|Quantum phase effect caused by electromagnetic potentials}}		{{Short description\|Quantum phase effect caused by electromagnetic potentials}}
	{{Quantum book backlink\|Quantum dynamics and evolution}}		{{Quantum book backlink\|Quantum dynamics and evolution}}
	{{Quantum article nav\|previous=Physics:Quantum Berry phase\|previous label=Berry phase\|next=Physics:Quantum Scattering theory\|next label=Scattering theory}}		{{Quantum article nav\|previous=Physics:Quantum Berry phase\|previous label=Berry phase\|next=Physics:Quantum Scattering theory\|next label=Scattering theory}}

	~~[[File~~:~~Quantum_aharonov_bohm_effect_yellow.png\|thumb\|280px\|Aharonov~~-~~Bohm phase shift around a shielded magnetic flux~~.]]		<div style="display:flex; gap:24px; align-items:flex-start; max-width:1280px; clear:both;">
			<div style="flex:1 1 680px; min-width:0; line-height:1.55;">
	The '''Quantum Aharonov-Bohm effect''' is a quantum phenomenon in which charged particles are affected by electromagnetic potentials even in regions where the classical electric and magnetic fields vanish. It demonstrates that potentials can have direct physical significance in [[Physics:Quantum mechanics\|quantum mechanics]].<ref>{{cite web \|url=https://en.wikipedia.org/wiki/Aharonov%E2%80%93Bohm_effect \|title=Aharonov-Bohm effect \|publisher=Wikipedia \|access-date=20 May 2026}}</ref>		The '''Quantum Aharonov-Bohm effect''' is a quantum phenomenon in which charged particles are affected by electromagnetic potentials even in regions where the classical electric and magnetic fields vanish. It demonstrates that potentials can have direct physical significance in [[Physics:Quantum mechanics\|quantum mechanics]].<ref>{{cite web \|url=https://en.wikipedia.org/wiki/Aharonov%E2%80%93Bohm_effect \|title=Aharonov-Bohm effect \|publisher=Wikipedia \|access-date=20 May 2026}}</ref>

	In the magnetic version, an electron wave is split into two paths around a confined magnetic flux. The electrons travel through field-free regions, but the vector potential changes their relative phase. When the paths recombine, the interference pattern shifts according to the enclosed magnetic flux.		In the magnetic version, an electron wave is split into two paths around a confined magnetic flux. The electrons travel through field-free regions, but the vector potential changes their relative phase. When the paths recombine, the interference pattern shifts according to the enclosed magnetic flux.
			</div>
			<div style="flex:0 0 380px; max-width:38%;">
			[[File:Quantum_aharonov_bohm_effect_yellow.png\|thumb\|360px\|Aharonov-Bohm phase shift around a shielded magnetic flux.]]
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			</div>

			<div style="clear:both;"></div>

	== Phase and potentials ==		== Phase and potentials ==

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	{{Short description\|Quantum phase effect caused by electromagnetic potentials}}		{{Short description\|Quantum phase effect caused by electromagnetic potentials}}
	{{Quantum book backlink\|Quantum dynamics and evolution}}		{{Quantum book backlink\|Quantum dynamics and evolution}}
			{{Quantum article nav\|previous=Physics:Quantum Berry phase\|previous label=Berry phase\|next=Physics:Quantum Scattering theory\|next label=Scattering theory}}

	[[File:Quantum_aharonov_bohm_effect_yellow.png\|thumb\|280px\|Aharonov-Bohm phase shift around a shielded magnetic flux.]]		[[File:Quantum_aharonov_bohm_effect_yellow.png\|thumb\|280px\|Aharonov-Bohm phase shift around a shielded magnetic flux.]]

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{{Short description|Quantum phase effect caused by electromagnetic potentials}}
{{Quantum book backlink|Quantum dynamics and evolution}}

[[File:Quantum_aharonov_bohm_effect_yellow.png|thumb|280px|Aharonov-Bohm phase shift around a shielded magnetic flux.]]

The '''Quantum Aharonov-Bohm effect''' is a quantum phenomenon in which charged particles are affected by electromagnetic potentials even in regions where the classical electric and magnetic fields vanish. It demonstrates that potentials can have direct physical significance in [[Physics:Quantum mechanics|quantum mechanics]].<ref>{{cite web |url=https://en.wikipedia.org/wiki/Aharonov%E2%80%93Bohm_effect |title=Aharonov-Bohm effect |publisher=Wikipedia |access-date=20 May 2026}}</ref>

In the magnetic version, an electron wave is split into two paths around a confined magnetic flux. The electrons travel through field-free regions, but the vector potential changes their relative phase. When the paths recombine, the interference pattern shifts according to the enclosed magnetic flux.

== Phase and potentials ==
Classically, only electric and magnetic fields exert forces on charged particles. In quantum theory, the phase of the wavefunction can respond to the vector potential itself. This makes the effect an important example of the phase sensitivity of quantum amplitudes.

The effect also connects naturally with [[Physics:Quantum Berry phase|geometric phase]], gauge fields, and topological descriptions of quantum systems.

== Significance ==
The Aharonov-Bohm effect is important in electron interferometry, mesoscopic physics, superconducting circuits, and discussions of gauge invariance. It shows that the quantum description cannot always be reduced to local classical forces acting along a path.

It also provides a clean conceptual bridge between [[Physics:Quantum Wavefunction|wavefunctions]], electromagnetic potentials, and [[Physics:Quantum gauge field|gauge fields]].

== See also ==
* [[Physics:Quantum Wavefunction]]
* [[Physics:Quantum Berry phase]]
* [[Physics:Quantum gauge field]]
* [[Physics:Quantum electromagnetic field]]

== References ==
{{reflist|3}}

{{Author|Harold Foppele}}

{{Sourceattribution|Physics:Quantum Aharonov-Bohm effect|1}}