Can anyone explain the process of quantum tunnneling?

Answer 1

In your chemistry class they probably showed you a picture of the electron 'cloud', where it is not a small sphere at a definite point, but more like a fog bank, where it has a given probability of being at any particular point.

Imagine such a fog bank with a wall passing through it near one edge*. The particle cannot exist inside the wall, but there is some probability of it existing on the other side. When something makes the particle have to decide just where it actually is [ie the wavefunction collapses][like when you open the box containing Schroedinger's cat and it has to be either alive or dead] some part of the time the electron will be outside the wall. Even though it could not be inside the wall, and could not pass through it, suddenly it is on the other side.

* Actually there isn't an edge; the probability cloud goes out to infinity, getting ever thinner. But typically an edge is shown to make visualization easier.

Quantum mechanics is a theory that is unreasonable, seemingly incomprehensible, and downright confusing, but it does have the redeeming feature that it accurately predicts measurable reality where other theories fail. And that latter bit is all that matters.

Answer 2

Think of localized solutions to the Schroedinger equation without potential, i.e. particles in vacuum: they are Gaussians. So every localized wave function can be thought of as "bulk" with tails. The tails "probe" the far environment beyond the bulk of the wave function. Even if you put up a (finite) potential wall, those tails will still extend beyond the wall with a finite probability. So the particle is constantly "probing" the conditions on the other side. How "often" this happens depends on how high and how wide the wall is. But once in a while the particle can be detected on the other side... and that's quantum tunneling. If the detection process is destructive, i.e. it absorbs the particle, the wave function will be completely collapsed and the particle can not go back on the other side, ever. That's what happens in strict cases of "tunneling", like alpha decay, where the alpha particle, after "getting out" of the nucleus is simply lost because it will move away from the positively charged nucleus.

Answer 3

A tunnel diode or Esaki diode is a type of semiconductor diode which is capable of very fast operation, well into the microwave region GHz, by utilizing quantum mechanical effects.

It was named after Leo Esaki, who in 1973 received the Nobel Prize in Physics for discovering the electron tunneling effect used in these diodes.

These diodes have a heavily doped p-n junction only some 10 nm (100 Å) wide. The heavy doping results in a broken bandgap, where conduction band electron states on the n-side are more or less aligned with valence band hole states on the p-side
Thus free electrons transition is possible across minimized potential barrier (doping effect)

Answer 4

If you have a potential barrier
U(x) = Uo, when 0 U(x) = 0, everyehere else,
you can take a particle of mass m, give the particle kinetic energy Ko = p²/2m < Uo, and see how it bounces off the barrier from the left.

In classical case nothing interesting happens, the particle bounces, but every child knows that.

In qunatum case you have to write wave function of the incident particle:
ψ(x) = exp(ip/ћ x), x<0
write Schrödinger equation
[-ћ²/2m ∂²/∂x² + U(x)]ψ = Eψ,
and see what happens.

Under the barrier the equation becomes
ћ²/2m ∂²/∂x² = (Uo - Ko)ψ,
and has solution
ψ(x) = Aexp(x/α) + Bexp(-x/α), where
α = ћ √[2m/(Uo - Ko)].

We can see that there is exponentially decaying tail of wave function ψ which penetrates to distance α. At right edge of the barrier wave function is approximately
ψ(x=+a) ≈ exp(aћ √[2m/(Uo - Ko)]), and its square, which is

probabilily of tunnelig is exp(2aћ √[2m/(Uo - Ko)])

Answer 5

yes (to what aman... said)
and to help understand you (teo) can look at
http://vergil.chemistry.gatech.edu/notes/quantrev/node20.html
and
http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/pbox.html#c3

it works the same as classical physics, in that the
total energy of a particle is = kinetic energy + potential energy
(which is what the schrodinger eqn says, but with the operators)
if you remember that, and look at the operators on the first link
you'll see what the 2nd link is saying, i hope. maybe it wont!
the tunneling arises since it is a necessary part of the solution to the equations..

Answer 6

quantum tunneling just a manifestation of particle wave duality.
It's a wave like process similar to diffraction which is not seen as what a particle would behave.