Quantum Tunneling through Potential Barriers - Revision history

Hari: /* Computational Model */

2026-04-27T17:17:14Z

Computational Model

← Older revision		Revision as of 13:17, 27 April 2026
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	The model below is an original GlowScript/Trinket visualization of quantum tunneling through a rectangular potential barrier. It lets the user change the particle energy <math>E</math>, barrier height <math>V_0</math>, and barrier width <math>L</math>. The model shows the oscillating wave before the barrier, the decaying wave inside the barrier, and the smaller transmitted wave after the barrier.		The model below is an original GlowScript/Trinket visualization of quantum tunneling through a rectangular potential barrier. It lets the user change the particle energy <math>E</math>, barrier height <math>V_0</math>, and barrier width <math>L</math>. The model shows the oscillating wave before the barrier, the decaying wave inside the barrier, and the smaller transmitted wave after the barrier.

	'''Original GlowScript/Trinket model:''' [https://trinket.io/embed/glowscript/caf10538764a Quantum Tunneling through a Rectangular Potential Barrier]		'''Original GlowScript/Trinket model:''' [https://trinket.io/embed/glowscript/caf10538764a?start=result Quantum Tunneling through a Rectangular Potential Barrier]

			<iframe src="https://trinket.io/embed/glowscript/caf10538764a?start=result"
			width="100%"
			height="500"
			frameborder="0"
			marginwidth="0"
			marginheight="0"
			allowfullscreen>
			</iframe>

	~~<iframe src="https://trinket.io/embed/glowscript/caf10538764a?start=result" width="100%" height="356" frameborder="0" marginwidth="0" marginheight="0" allowfullscreen></iframe>~~
	If the embedded model does not load inside the wiki, open the linked Trinket model above in a new tab. This model was created for this page and is meant to show the main qualitative idea: the wavefunction does not instantly become zero inside the barrier. It decays, and the amount left on the far side depends strongly on the barrier height, barrier width, and particle energy.		If the embedded model does not load inside the wiki, open the linked Trinket model above in a new tab. This model was created for this page and is meant to show the main qualitative idea: the wavefunction does not instantly become zero inside the barrier. It decays, and the amount left on the far side depends strongly on the barrier height, barrier width, and particle energy.

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	* Increase the barrier width and observe how the transmitted wave decreases.		* Increase the barrier width and observe how the transmitted wave decreases.
	* Increase the barrier height and observe how the transmitted wave decreases.		* Increase the barrier height and observe how the transmitted wave decreases.
	* Compare a plane wave with a wave packet.==Common Exam Mistakes==		* Compare a plane wave with a wave packet.

			==Common Exam Mistakes==

	* '''Thinking tunneling is classically allowed.''' If <math>E<V_0</math>, classical mechanics predicts no transmission. Tunneling is a quantum effect.		* '''Thinking tunneling is classically allowed.''' If <math>E<V_0</math>, classical mechanics predicts no transmission. Tunneling is a quantum effect.

Hari at 17:15, 27 April 2026

2026-04-27T17:15:57Z

← Older revision		Revision as of 13:15, 27 April 2026
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	Since the exponential term is <math>e^{-2\kappa L}</math>, even a small increase in barrier width can cause a huge decrease in tunneling probability.		Since the exponential term is <math>e^{-2\kappa L}</math>, even a small increase in barrier width can cause a huge decrease in tunneling probability.

			==Computational Model==

	The model below is an original GlowScript/Trinket visualization of quantum tunneling through a rectangular potential barrier. It lets the user change the particle energy <math>E</math>, barrier height <math>V_0</math>, and barrier width <math>L</math>. The model shows the oscillating wave before the barrier, the decaying wave inside the barrier, and the smaller transmitted wave after the barrier.		The model below is an original GlowScript/Trinket visualization of quantum tunneling through a rectangular potential barrier. It lets the user change the particle energy <math>E</math>, barrier height <math>V_0</math>, and barrier width <math>L</math>. The model shows the oscillating wave before the barrier, the decaying wave inside the barrier, and the smaller transmitted wave after the barrier.

	~~<iframe src="~~https://trinket.io/embed/glowscript/caf10538764a"		'''Original GlowScript/Trinket model:''' [https://trinket.io/embed/glowscript/caf10538764a Quantum Tunneling through a Rectangular Potential Barrier]
	~~width="900"~~
	~~height="600"~~
	~~frameborder="0"~~
	~~marginwidth="0"~~
	~~marginheight="0"~~
	~~allowfullscreen>~~
	~~</iframe>~~

	~~The simulation~~ is meant to show the main qualitative idea: the wavefunction does not instantly become zero inside the barrier. It decays, and the amount left on the far side depends strongly on the barrier height, barrier width, and particle energy.		<iframe src="https://trinket.io/embed/glowscript/caf10538764a?start=result" width="100%" height="356" frameborder="0" marginwidth="0" marginheight="0" allowfullscreen></iframe>
			If the embedded model does not load inside the wiki, open the linked Trinket model above in a new tab. This model was created for this page and is meant to show the main qualitative idea: the wavefunction does not instantly become zero inside the barrier. It decays, and the amount left on the far side depends strongly on the barrier height, barrier width, and particle energy.

	The PhET quantum tunneling simulation below is also useful because it lets users compare plane waves and wave packets for different potential shapes.		The PhET quantum tunneling simulation below is also useful because it lets users compare plane waves and wave packets for different potential shapes.
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	* Increase the barrier width and observe how the transmitted wave decreases.		* Increase the barrier width and observe how the transmitted wave decreases.
	* Increase the barrier height and observe how the transmitted wave decreases.		* Increase the barrier height and observe how the transmitted wave decreases.
	* Compare a plane wave with a wave packet.		* Compare a plane wave with a wave packet.==Common Exam Mistakes==

	==Common Exam Mistakes==

	* '''Thinking tunneling is classically allowed.''' If <math>E<V_0</math>, classical mechanics predicts no transmission. Tunneling is a quantum effect.		* '''Thinking tunneling is classically allowed.''' If <math>E<V_0</math>, classical mechanics predicts no transmission. Tunneling is a quantum effect.

Hari: /* Computational Model */

2026-04-27T17:13:35Z

Computational Model

← Older revision		Revision as of 13:13, 27 April 2026
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	Since the exponential term is <math>e^{-2\kappa L}</math>, even a small increase in barrier width can cause a huge decrease in tunneling probability.		Since the exponential term is <math>e^{-2\kappa L}</math>, even a small increase in barrier width can cause a huge decrease in tunneling probability.

	~~==Computational Model==~~

	The model below is an original GlowScript/Trinket visualization of quantum tunneling through a rectangular potential barrier. It lets the user change the particle energy <math>E</math>, barrier height <math>V_0</math>, and barrier width <math>L</math>. The model shows the oscillating wave before the barrier, the decaying wave inside the barrier, and the smaller transmitted wave after the barrier.		The model below is an original GlowScript/Trinket visualization of quantum tunneling through a rectangular potential barrier. It lets the user change the particle energy <math>E</math>, barrier height <math>V_0</math>, and barrier width <math>L</math>. The model shows the oscillating wave before the barrier, the decaying wave inside the barrier, and the smaller transmitted wave after the barrier.

Hari at 17:11, 27 April 2026

2026-04-27T17:11:34Z

← Older revision		Revision as of 13:11, 27 April 2026
Line 177:		Line 177:
	The model below is an original GlowScript/Trinket visualization of quantum tunneling through a rectangular potential barrier. It lets the user change the particle energy <math>E</math>, barrier height <math>V_0</math>, and barrier width <math>L</math>. The model shows the oscillating wave before the barrier, the decaying wave inside the barrier, and the smaller transmitted wave after the barrier.		The model below is an original GlowScript/Trinket visualization of quantum tunneling through a rectangular potential barrier. It lets the user change the particle energy <math>E</math>, barrier height <math>V_0</math>, and barrier width <math>L</math>. The model shows the oscillating wave before the barrier, the decaying wave inside the barrier, and the smaller transmitted wave after the barrier.

	~~<iframe src="~~<iframe src="https://trinket.io/embed/glowscript/caf10538764a~~" width="100%" height="356" frameborder="0" marginwidth="0" marginheight="0" allowfullscreen></iframe>~~"		<iframe src="https://trinket.io/embed/glowscript/caf10538764a"
	width="900"		width="900"
	height="600"		height="600"
			frameborder="0"
			marginwidth="0"
			marginheight="0"
	allowfullscreen>		allowfullscreen>
	</iframe>		</iframe>
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	width="800"		width="800"
	height="600"		height="600"
			frameborder="0"
			marginwidth="0"
			marginheight="0"
	allowfullscreen>		allowfullscreen>
	</iframe>		</iframe>

Hari at 17:09, 27 April 2026

2026-04-27T17:09:03Z

← Older revision		Revision as of 13:09, 27 April 2026
Line 177:		Line 177:
	The model below is an original GlowScript/Trinket visualization of quantum tunneling through a rectangular potential barrier. It lets the user change the particle energy <math>E</math>, barrier height <math>V_0</math>, and barrier width <math>L</math>. The model shows the oscillating wave before the barrier, the decaying wave inside the barrier, and the smaller transmitted wave after the barrier.		The model below is an original GlowScript/Trinket visualization of quantum tunneling through a rectangular potential barrier. It lets the user change the particle energy <math>E</math>, barrier height <math>V_0</math>, and barrier width <math>L</math>. The model shows the oscillating wave before the barrier, the decaying wave inside the barrier, and the smaller transmitted wave after the barrier.

	<iframe src="~~PASTE_YOUR_TRINKET_EMBED_URL_HERE~~"		<iframe src="<iframe src="https://trinket.io/embed/glowscript/caf10538764a" width="100%" height="356" frameborder="0" marginwidth="0" marginheight="0" allowfullscreen></iframe>"
	width="900"		width="900"
	height="600"		height="600"

Hari at 17:05, 27 April 2026

2026-04-27T17:05:13Z

← Older revision		Revision as of 13:05, 27 April 2026
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	The important point is that tunneling is probabilistic. We cannot say exactly when one particle will tunnel, but we can calculate the probability that it will.		The important point is that tunneling is probabilistic. We cannot say exactly when one particle will tunnel, but we can calculate the probability that it will.

	[[File:Quantum-tunneling.~~svg~~\|thumb\|center\|500px\|Quantum tunneling through a square potential barrier. The diagram shows an incoming wave encountering a finite barrier and a smaller transmitted wave appearing on the far side. Image by MikeRun, licensed under Creative Commons Attribution-ShareAlike 4.0 International, via Wikimedia Commons.]]		[[File:Quantum-tunneling.png\|thumb\|center\|500px\|Quantum tunneling through a square potential barrier. The diagram shows an incoming wave encountering a finite barrier and a smaller transmitted wave appearing on the far side. Image by MikeRun, licensed under Creative Commons Attribution-ShareAlike 4.0 International, via Wikimedia Commons.]]

	===Classical Expectations===		===Classical Expectations===

Hari at 17:02, 27 April 2026

2026-04-27T17:02:17Z

← Older revision		Revision as of 13:02, 27 April 2026
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	The important point is that tunneling is probabilistic. We cannot say exactly when one particle will tunnel, but we can calculate the probability that it will.		The important point is that tunneling is probabilistic. We cannot say exactly when one particle will tunnel, but we can calculate the probability that it will.

	[[File:~~QuantumTunnelingBarrier_Haripratiik_Spring2026~~.svg\|thumb\|center\|~~800px~~\|~~Original diagram of quantum~~ tunneling through a ~~finite rectangular~~ potential barrier. ~~In Region I, the~~ wave ~~has incident~~ and ~~reflected parts. In Region II, the wavefunction decays exponentially. In Region III,~~ a smaller transmitted wave ~~appears~~. ~~Diagram created~~ by ~~Haripratiik Arunkumar Malarkodi~~, ~~Spring 2026~~.]]		[[File:Quantum-tunneling.svg\|thumb\|center\|500px\|Quantum tunneling through a square potential barrier. The diagram shows an incoming wave encountering a finite barrier and a smaller transmitted wave appearing on the far side. Image by MikeRun, licensed under Creative Commons Attribution-ShareAlike 4.0 International, via Wikimedia Commons.]]

	===Classical Expectations===		===Classical Expectations===
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	==External Resources==		==External Resources==

			* [https://commons.wikimedia.org/wiki/File:Quantum-tunneling.svg Wikimedia Commons: Quantum-tunneling.svg]
	* [https://phet.colorado.edu/en/simulations/quantum-tunneling PhET: Quantum Tunneling and Wave Packets]		* [https://phet.colorado.edu/en/simulations/quantum-tunneling PhET: Quantum Tunneling and Wave Packets]
	* [https://openstax.org/books/university-physics-volume-3/pages/7-6-the-quantum-tunneling-of-particles-through-potential-barriers OpenStax: Quantum Tunneling of Particles through Potential Barriers]		* [https://openstax.org/books/university-physics-volume-3/pages/7-6-the-quantum-tunneling-of-particles-through-potential-barriers OpenStax: Quantum Tunneling of Particles through Potential Barriers]
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	==References==		==References==

			* MikeRun, ''Quantum-tunneling.svg'', Wikimedia Commons. Licensed under Creative Commons Attribution-ShareAlike 4.0 International.
	* OpenStax, ''University Physics Volume 3'', Chapter 7: Quantum Mechanics. Licensed under Creative Commons Attribution 4.0 International.		* OpenStax, ''University Physics Volume 3'', Chapter 7: Quantum Mechanics. Licensed under Creative Commons Attribution 4.0 International.
	* LibreTexts, ''Quantum Tunneling of Particles through Potential Barriers''.		* LibreTexts, ''Quantum Tunneling of Particles through Potential Barriers''.
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	* PhET Interactive Simulations, ''Quantum Tunneling and Wave Packets''.		* PhET Interactive Simulations, ''Quantum Tunneling and Wave Packets''.
	* Original GlowScript/Trinket model by Haripratiik Arunkumar Malarkodi, Spring 2026.		* Original GlowScript/Trinket model by Haripratiik Arunkumar Malarkodi, Spring 2026.
	* Original barrier diagram by Haripratiik Arunkumar Malarkodi, Spring 2026.

	[[Category: Quantum Mechanics]]		[[Category: Quantum Mechanics]]

Hari at 16:55, 27 April 2026

2026-04-27T16:55:09Z

Show changes

Hari at 16:25, 27 April 2026

2026-04-27T16:25:01Z

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Joshykim: /* References */

2025-12-02T21:20:22Z

References

← Older revision		Revision as of 17:20, 2 December 2025
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	* [[Quantum Wells and Bound States]]		* [[Quantum Wells and Bound States]]

	===~~References~~===		===External Resources===
	* [https://~~openstax~~.~~org~~/~~details~~/~~books~~/~~university-physics-volume~~-3]		* [https://phet.colorado.edu/en/simulations/quantum-tunneling]
	* [~~http~~://~~hyperphysics.phy-astr~~.~~gsu~~.~~edu~~/~~hbase/hframe.html~~]		* [https://www.youtube.com/watch?v=cTodS8hkSDg]
	* [https://~~physicstoday~~.~~scitation~~.~~org~~/~~doi/10.1063/1.1510281~~]		* [https://www.youtube.com/watch?v=RF7dDt3tVmI]

	==References==		==References==