## Quantum Mechanics: Tunneling

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#### Abstract

In quantum mechanics, quantum tunnelling is a micro nanoscopic phenomenon in which a particle violates the principles of classical mechanics by penetrating a potential barrier or impedance higher than the kinetic energy of the particle. A barrier, in terms of quantum tunnelling, may be a form of energy state analogous to a "hill" or incline in classical mechanics, which classically suggests that passage through or over such a barrier would be impossible without sufficient energy. The two remarkable applications of tunneling are:

- (a)Resonant tunneling diodes, which are used as switching units in fast electronic circuits.
- (b) Scanning tunneling microscope (STM), based on the penetration of electrons near the surface of a solid sample through the barrier at the surface. These electrons form a "cloud" of probability outside the sample. Although the probability of detecting one of these electrons decays exponentially with distance (from the surface), one can induce and measure a current of these electrons and attain a magnification factor of 100 million - large enough to permit resolution of a few hundredths the size of an atom. Gerd Binning and Heinrich Rohrer won the Noble Prize in Physics in 1986 for the invention of the STM.

To better understand the tunneling phenomena below we provide relevant reading material and access to the piece-wise constant potential barrier tool that contains examples for calculation of the tunneling coefficient in quite a variety of structures:

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