Quantum Tunneling

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Quantum tunneling refers to the instance when a particle breaks through a barrier that is normally impassible. The basis of Quantum tunneling and how it functions can be summed up in this equation: (change in E)(change in t) = h. Although we can't change the total amount of energy without violating the law of conservation of energy, we can "borrow" some energy (change in E) to get over the barrier as long as we repay it in time: (change in t) = h / (change in E). The reason a particle can do this is that we cannot accurately know the energy of a particle. It is instead expressed as an uncertainty: (change in E) = h / (change in t). Of course, if the barrier is too wide or tall, the chances of quantum tunneling occurring becomes scare because of the increased time needed needed to repay the amount of energy borrowed. (Quantum Universe)

Funnily enough, waves share a quantum tunneling like component to them as well. If we were to increase the angle above a glass block's critical angle, we achieve total-internal reflection caused by a standing wave that does not transmit any light energy. This means all of the light that would exit the glass block before the critical angle is instead kept within the glass block, hence the name. If we were to place another glass block next to the existing one with the total-internal reflection, you will see that light somehow travels into the added block, even though there is supposed to be total-internal reflection. The reason for that is the amplitude of the standing wave in the "forbidden" gap hasn't fully decayed. This phenomena is referred to as frustrated total-internal reflection. (Quantum Universe)

The Scanning Tunneling Microscope (STM) works almost in the same way as the light waves do. The machine takes advantage of the "vacuum tunneling" property of electrons in order to study the surface of materials. Electrons in a solid have a small chance of appearing outside of the metal surface. Much like the...
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