Quantum tunneling is responsible for many important phenomena such as
the alpha decay of atomic nuclei and the operation of certain types of diodes.
Yet, quantum tunneling is completely contrary to our intuition
about how the universe is supposed to work.
This is because quantum tunneling
has absolutely no analogy in classical physics.
To understand quantum tunneling, we must understand that
particles do not have a defined position until they are observed.
Instead, all particles are described by what we call a “wave function.”
The probability of a particle being observed at a particular location is given by
the square of the amplitude of the wave function at that location.
In this example, the red sphere represents the most
probable location where we will observe the particle,
because this is where the amplitude is greatest.
Suppose that the particle bounces off a barrier,
where the energy of the barrier is greater than the energy of the particle.
This is represented by the wave function reflecting at the boundary.
Let’s take a look at how the wave function behaves inside the barrier.
As the distance into the barrier increases,
the amplitude of the wave function decreases exponentially.
But, the wave function does not actually reach an amplitude of zero.
Now, let us consider a new scenario where the barrier is shorter in length.
As before, the amplitude of the wave function will decay inside the barrier.
But, since the wave function does not reach an amplitude of zero,
the wave function can exit the barrier on the other side.
Once the wave function exits the barrier, its amplitude no longer decays.
A portion of the wave function passes through each of the two boundaries.
And a portion of the wave function also reflects at each of the two boundaries.
This means that there is a certain probability that the particle
will pass through the barrier to the other side,
and a certain probability that the particle will bounce off the barrier.
If we send a number of these particles towards the barrier,
some of them will pass through, and some of them will bounce off.
If we send a number of these particles towards the barrier,
some of them will pass through, and some of them will bounce off.
Now let us consider yet another scenario where the barrier’s length is even shorter.
In this case,
the wave function doesn’t have as much distance to decay inside the barrier,
and we therefore have a larger amplitude
for the portion of the wave function that exits the barrier.
This means that with this shorter barrier,
the particle has a greater probability of passing through.
It also means that the particle has a lower probability of bouncing off the barrier,
which is represented by a smaller amplitude for the reflected wave.
As we increase the length of the barrier,
the particle is less likely to pass through, and more likely to bounce off.
But, even if the probability of each individual particle
passing through a barrier is small, with a large number of particles,
there is a high probability that at least some of them will pass through.
From the perspective of classical physics,
if the energy of the barrier is greater than the energy of the incoming particles,
then there is no possibility that any of the particles will make it past the boundary.
But from the perspective of quantum mechanics,
it is a very different world, and hence we have what we call quantum tunneling.
Much more detailed information on quantum mechanics
can be found in the other videos on this channel.
Please subscribe to be notified when new videos are ready.