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QuantumTunneling

Ashley Gnoss & Kyle Kucker

Physics 43/ May 10th, 011

!anta "osa #unior $ollege !%ring 11Image: http://www.google.com/imgres?imgurl=http://www.colorado.edu/physics/phys3220/phys3220

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Introduction to the concept

Quantum tunneling is one of thephenomena displaying the odd natureof Quantum Mechanics.

It concerns particles in their wavestates, where each observable can bedescribed most acutely by a distributionof probability.

This is the main point, that there is nopoint.

Classically, it is assumed that particlesthat we can observe to be point-likeshould behave as if under the rules thatgovern the more massive objects thatwe have encountered, that is, theyshould behave deterministically.

But due to the nature of QuantumMechanics, there is a magnitude of sizeand complexity for which the rulesseem to change.

Image:http://www.lightandmatter.com/html_books/6mr/ch05/figs/big-hydrogen-wavefunction.jpg

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Quantum Mechanics: Introduction to the Concept Particles that we had assumed to be

definite in their properties, (position,energy, time, momentum) can only

be described as distributions ofprobability.

These distributions have anotherlimitation. Due to our methods ofdetection, we are restricted to neverknowing two properties of a particlesimultaneously. We can neverunderstand fully (with our currentknowledge) what the particle/distribution is doing, nor predict whatit will do.

This is the reason why we do not yetknow what to call these objects. Waves

or particles. Quantum mechanics emphasizes the

wave-nature, because it is throughwave mechanics that we can describethese probability distributions andhow they could be an adequate

description of the particle, though anunintuitive one.

A few wave distributions of a

hydrogen atom, describing varying

positions (or potential positions) of

the electron.

Image: http://upload.wikimedia.org/wikipedia/

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'eisen(erg)s *ncertainty Princi%le

The inability to know certain multipleproperties of an object at the same

time is due to the uncertainty

principle.

This principle is the concept behind

quantum tunneling.

It is due to this lack of knowledge

about the particle that we call the

action of tunneling an odd

phenomena.

Indeed, it makes describing the rules

and properties of nature a much more

complex activity than once thought.

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If the properties of the atom

and particle could be knownwith certainty, then they

would decohere and their

wave behavior and their

ability to interfere would be

destroyed- An interpretation

of Quantum Mechanics

.uations o the*ncertainty Princi%le

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The Tunneling o a Particle

Tunneling refers to the ability of aparticle to overcome and cross apotential energy barrier that it would not

be able do based on classicalunderstanding.

It is only the particles wave-nature thatallows for this phenomenon.

The probability wave describing theparticles position is an integral that

overlaps into the energy barrier, allowingfor some finite probability that the

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Tunneling in ature Our sun persists in keeping us

warm (and alive) through the

process of fusion. Fusion is thecreation of larger atomicnuclei/elements from smallerones.

Fusion occurs only at extremelyhigh temperatures, where the

Kinetic Energy is high enough toovercome the potential barrierdue to the repelling of thenucleons.

The only thing is that our sun isnot hot enough to produce thesehigh energies.

Tunneling is the explanation.Only due to the overlap of theprobability waves of the nucleican they overcome the barrier

separating them and fuse.

Radioactive decay is another example

of how tunneling circumvents the

tendencies of nature.

Particles such as alpha particles are held

in the nucleus by the strong force,

which means that they shouldnt be able

to escape. Tunneling again explains

how the particles are able to overcomethe strongest known force in nature.

In the case of the alpha particle for

instance, the location of the particle

within the nucleus is fairly accurately

known, and due to the uncertaintyprinciple, the probability wave for the

velocity (and therefore kinetic energy)

is greater. The property unable to be

defined and the wave description gives

it a finite probability to arrive outside of

the nucleus.

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Technological A%%lications Once of the most important uses of electron

tunneling is the production of current.

A new and interesting use is within the new

touch screen phones. By applying a force (pressure with the

finger), the layers particles of polymerwithin the screen come closer together.

Before they are moved together there is alarge enough vacuum between the layers

and so that the probability of electronstunneling from one layer to another is verylow.

By exerting force on the layers, we are ableto bring the probability waves of theelectrons closer together, increasing the rate

of tunneling, enough to produce current on-demand, changing the material from aninsulator to a metal.

The change in tunneling is extreme. Forevery Angstrom closer (1/10th of ananometer) the rate of tunneling increasesby ten times. And the resistance changes

from 10^12 ohms to 1 ohm!

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Sources

New Ideas in Quantum Tunneling.http://www.technologyreview.com/blog/arxiv/23409/

Explanation of simple concept.http

://abyss.uoregon.edu/~js/glossary/quantum_tunneling.html

Lecture

onQuantumTunneling.http://www.youtube.com/wat

ch?v=vMndTqowzqU

http://www-istp.gsfc.nasa.gov/stargaze/Q8.htm

Molecular vibration-sensing component in

Drosophila melanogaster

olfaction).

(All researched May 5, 2011)