How does a particle tunnels through a barrier?

Answer 1

In a purely classical world, the probability of a moving particle getting through an electro-static barrier was simple: if the kinetic energy of the particle was greater than the charge times the voltage, it was 100% likely to get through, if the KE was less, the probability was zero. In the latter case, the ball would simply bounce back, because the energy level of the voltage barrier ( 'E(vb)' ) was simply too large for that particle's KE to overcome

When you do the mathematics of the Schroendinger Equation with this situation -- a charged particle meeting a voltage barrier -- you can no longer talk about what WILL happen with 100% certainty. You can only discuss the PROBABILITY of something happening. For example, even if the electron has more KE than E(bv), then there is some chance that it will bounce back.

When a moving electron meets a voltage barrier, in which the initial KE is smaller than E(vb), then the probability of finding that electron in that barrier goes down fairly rapidly. If the barrier is thick, then the probability of finding the electron in that area of high voltage goes down to zero. On the other hand, it CAN happen that, for a thin barrier (or a fast electron or a voltage barrier not too large), that the probability of finding an electron beyond the barrier does NOT go down to zero. In that case, you have quantum tunnelling.

The mathematics are fairly complicated; but have been shown to agree with experiment.