## Friday, October 14, 2011

### Quantum Tunneling from Quantum Mechanics

he process by which a particle gets across a barrier that it can not classically pass. Quantum Tunneling is related to Wave-particle duality because it results from the wave nature of a particle. The probability of the particle getting through the barrier drops exponentially with the thickness of the barrier.

When the wave comes in contact with the barrier most of it bounces off the carrier but a small amount passes through the barrier; but that amount decays exponentially with the thickness of the barrier.  Such that the amplitude of the initial wave increases then the amplitude of the wave on the opposite side of the barrier increases. If the barrier thickness increases, the amplitude of the wave on the opposite side of the barrier decreases. If the energy of the initial wave increases, (wavelength decreases) the amplitude of the wave on the opposite side of the barrier increases. If the waves energy greater than that of the barrier it will all pass through the barrier. With a longer wavelength For particles most of them bounce off while a few instantly get through.

Quantum tunneling is theoretically valid at the macroscopic but the odds of it occurring are extremely small. For example there is a non zero probability that you could run your car into a brick wall an suddenly find yourself safely on the other side. However please don’t try it because the odds that it will happen are so small as to be impossible by any reasonable definition.

Tunneling gets subatomic particles across barriers they normally can not cross. The number of particles that gets across the barrier drops exponentially with the barrier thickness. The number of particles that gets across the barrier increases with the energy of the particle. Quantum tunneling is a purely quantum effect. It has no counter part in Classical mechanics. It could theoretically occur on the macroscopic scale but the odds are too small to ever see it happen.