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By the end of this section, you will be able to:
  • Describe how a quantum particle may tunnel across a potential barrier
  • Identify important physical parameters that affect the tunneling probability
  • Identify the physical phenomena where quantum tunneling is observed
  • Explain how quantum tunneling is utilized in modern technologies

Quantum tunneling is a phenomenon in which particles penetrate a potential energy barrier with a height greater than the total energy of the particles. The phenomenon is interesting and important because it violates the principles of classical mechanics. Quantum tunneling is important in models of the Sun and has a wide range of applications, such as the scanning tunneling microscope and the tunnel diode.

Tunneling and potential energy

To illustrate quantum tunneling    , consider a ball rolling along a surface with a kinetic energy of 100 J. As the ball rolls, it encounters a hill. The potential energy of the ball placed atop the hill is 10 J. Therefore, the ball (with 100 J of kinetic energy) easily rolls over the hill and continues on. In classical mechanics, the probability that the ball passes over the hill is exactly 1—it makes it over every time. If, however, the height of the hill is increased—a ball placed atop the hill has a potential energy of 200 J—the ball proceeds only part of the way up the hill, stops, and returns in the direction it came. The total energy of the ball is converted entirely into potential energy before it can reach the top of the hill. We do not expect, even after repeated attempts, for the 100-J ball to ever be found beyond the hill. Therefore, the probability that the ball passes over the hill is exactly 0, and probability it is turned back or “reflected” by the hill is exactly 1. The ball never makes it over the hill. The existence of the ball beyond the hill is an impossibility or “energetically forbidden.”

However, according to quantum mechanics, the ball has a wave function and this function is defined over all space. The wave function may be highly localized, but there is always a chance that as the ball encounters the hill, the ball will suddenly be found beyond it. Indeed, this probability is appreciable if the “wave packet” of the ball is wider than the barrier.

View this interactive simulation for a simulation of tunneling.

In the language of quantum mechanics, the hill is characterized by a potential barrier    . A finite-height square barrier is described by the following potential-energy function:

U ( x ) = { 0 , when x < 0 U 0 , when 0 x L 0 , when x > L .

The potential barrier is illustrated in [link] . When the height U 0 of the barrier is infinite, the wave packet representing an incident quantum particle is unable to penetrate it, and the quantum particle bounces back from the barrier boundary, just like a classical particle. When the width L of the barrier is infinite and its height is finite, a part of the wave packet representing an incident quantum particle can filter through the barrier boundary and eventually perish after traveling some distance inside the barrier.

Questions & Answers

how does colour appear in thin films
Nwjwr Reply
in the wave equation y=Asin(kx-wt+¢) what does k and w stand for.
Kimani Reply
derivation of lateral shieft
James Reply
how are you?
I'm fine
total binding energy of ionic crystal at equilibrium is
All Reply
How does, ray of light coming form focus, behaves in concave mirror after refraction?
Bishesh Reply
Refraction does not occur in concave mirror. If refraction occurs then I don't know about this.
What is motion
Izevbogie Reply
Anything which changes itself with respect to time or surrounding
and what's time? is time everywhere same
how can u say that
do u know about black hole
Not so more
Radioactive substance
These substance create harmful radiation like alpha particle radiation, beta particle radiation, gamma particle radiation
But ask anything changes itself with respect to time or surrounding A Not any harmful radiation
explain cavendish experiment to determine the value of gravitational concept.
Celine Reply
For the question about the scuba instructor's head above the pool, how did you arrive at this answer? What is the process?
Evan Reply
as a free falling object increases speed what is happening to the acceleration
Success Reply
of course g is constant
acceleration also inc
which paper will be subjective and which one objective
normal distributiin of errors report
normal distribution of errors
acceleration also increases
there are two correct answers depending on whether air resistance is considered. none of those answers have acceleration increasing.
Acceleration is the change in velocity over time, hence it's the derivative of the velocity with respect to time. So this case would depend on the velocity. More specifically the change in velocity in the system.
photo electrons doesn't emmit when electrons are free to move on surface of metal why?
Rafi Reply
What would be the minimum work function of a metal have to be for visible light(400-700)nm to ejected photoelectrons?
Mohammed Reply
give any fix value to wave length
40 cm into change mm
Arhaan Reply
40cm=40.0×10^-2m =400.0×10^-3m =400mm. that cap(^) I have used above is to the power.
i.e. 10to the power -2 in the first line and 10 to the power -3 in the the second line.
there is mistake in my first msg correction is 40cm=40.0×10^-2m =400.0×10^-3m =400mm. sorry for the mistake friends.
40cm=40.0×10^-2m =400.0×10^-3m =400mm.
this msg is out of mistake. sorry friends​.
what is physics?
sisay Reply
why we have physics
Anil Reply
because is the study of mater and natural world
because physics is nature. it explains the laws of nature. some laws already discovered. some laws yet to be discovered.
physics is the study of non living things if we added it with biology it becomes biophysics and bio is the study of living things tell me please what is this?
physics is the study of matter,energy and their interactions
all living things are matter
why rolling friction is less than sliding friction
thanks buvanas
is this a physics forum
Physics Reply

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Source:  OpenStax, University physics volume 3. OpenStax CNX. Nov 04, 2016 Download for free at http://cnx.org/content/col12067/1.4
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