Quantum+Tunnelling


 * Quantum Tunneling **

Quantum tunneling, also called barrier penetration is another of the bizarre phenomena that only take place in the quantum world.

Consider the following example. For a ball to roll up a hill and down the other side, it has to be given enough energy to begin with. As it climbs the slope, it will gradually slow down and unless it has enough energy to reach the top, it will stop and roll back again.

However, if the ball were to behave quantum-mechanically, there would always be a certain probability that it would spontaneously disappear from one side of the hill and reappear on the other side. This would happen despite it not have sufficient energy to have reached the top to go the conventional way.

The standard way of explaining how quantum tunneling takes place is by appealing to Heisenberg’s uncertainty relation between energy and time. Provided the energy barrier that a particle needs to tunnel through is not too high or wide, it can borrow sufficient energy from its surroundings to get through. This is allowed as long as it gives back this energy within a time set by the uncertainty relation.

More accurately, we must think of the particle’s wavefunction as existing as a superposition of being on both sides of the barrier at once. This is the wavefunction that penetrates the barrier. Only when we look do we collapse the wavefunction to find the particle on one side or the other.