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Quantum Tunneling in Quantum Physics


Quantum tunneling: The process by which a particle gets across a barrier that it can not classically pass.

Quantum Tunneling is related to Wave-particle duality in that it is a result of the wave nature of a particle. The probability of the particle getting through the barrier drops exponentially with the thickness of the barrier.

Y(x) =  Y(0)e-kx

Y - the wave function

e – the natural log base number.

k - particles wave number inside the barrier.

x - The distance from the start of the barrier.

m – Particle’s mass

E – Particle’s Energy

V – Barrier’s Energy

h = 6.626 X 10-34 J * S
Planck's constant

The results are that when the wave comes in contact with the barrier most of it bounces off the carrier but some passes through the barrier; however it decays exponentially with the thickness of the barrier.

As the amplitude of the initial wave increases then the amplitude of the wave on the opposite side of the barrier increases.

As the barrier thickness increases, the amplitude of the wave on the opposite side of the barrier decreases.

As 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 tts all passes through the barrier but with a longer wavelength

For particles most of them bounce off while a few instantly get through.

Particle Barrier

The shorter the barrier the more particles get through.

If the barrier is thicker fewer get through.

If the barrier is even thicker even fewer get through.

Particle Velocity

The slower the particles the fewer get through

Speed up the particles and more particles get through.

If the particles’ speed is such that their energy exceeds that of the barrier then almost all of the particles cross the barrier but they do so at a slower speed.

In conclusion 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.

One interring aspect aspect of quantum tunneling is that the particle that cross the barrier do so literally instantaneously. That's right they take absolutely no time to cross the barrier, they just skip over that space entirely. That is just another weird aspect of quantum mechanics. Things can intently go from place to place with out going through the space in between.


 

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