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Quantum tunneling of the quantum mechanics

Wave-particle duality

 Automatic translation  Automatic translation Updated December 16, 2012

To understand the quantum tunneling, it must return to the wave-particle duality of quantum mechanics.
In 1911, Ernest Rutherford (1871 − 1937) specifies the structure of the atom and gives the atomic nucleus size of about 10-14 meters, the smallness of this size is difficult to imagine in our mind, but it is in these dimensions that laws quantum mechanics are expressed. In classical physics the atoms are constituted of a certain number of negatively charged electrons spot and a point-like nucleus, positively charged, but it raises a paradox. The matter should disappear, annihilate itself, because an electron witch radiates around nucleus loses energy (James Clerk Maxwell's theory) and therefore should fall on the nucleus. This means that the stability of an atom is incomprehensible in the context of the classical theory. By cons, quantum physics explains the mystery of the atom and the stability of the matter. Quantum physics has appeared between 1925 and 1927, derived from quantum mechanics initiated by Max Planck (1858 − 1947) in 1900 and developed by the great scientists of the early twentieth century between 1905 and 1924, Einstein, Bohr, Sommerfeld, Kramers, Heisenberg, Pauli and de Broglie. In the field of the infinitely small a particle behaves as both a particle and a wave. Quantum theory is a theory by definition non-deterministic, i.e. that even if we know all the parameters at the start, there are phenomena that we can not predict.


This uncertainty and indeterminacy that are intrinsic to the theory and thus to subatomic particles, constituents of matter. In addition to the uncertainty about the locality, quantum mechanics tolerate the existence of entangled states, i.e. at the quantum level several spatially separated objects can form a single quantum object, which react together, it is important to foresee the tunnel effect. In summary, in the quantum world, the subatomic particles, objects can be both here and there, in a state or another. We can not determine the status of a 'quantum system' except by observing it, which has the effect of destroying the state in question.
Quantum mechanics, never falling until today, explains the existence of matter. This is the great intellectual adventure of the 20th century, but we had pictures to represent the structure of quantum matter.
Since the invention of the first microscopes, man has always wanted to represent the microscopic world.
In 1981, two IBM researchers, Gerd Binnig and Heinrich Rohrer were able to 'see' very, very small dimensions of the atom when they invent the scanning tunneling microscope (STM), they get the Nobel Prize in Physics 1986.

NB: in 1928 the American physicist George Gamow discover the tunneling quantum mechanics.

 Iron atoms seen by a scanning tunneling microscope

Image: Image taken with a scanning tunneling microscope. This image is about 5 nanometers shows a copper surface where the copper atoms are contained within an enclosure quantum of 48 iron atoms. The circular barrier iron has a radius of 71.3 Angstroms (71.3 x10-10) meter. We see the electrons behave like waves.
© IBM Almaden Visualization Lab

Scanning tunneling microscope (STM)


The STM is widely regarded as the instrument that opened the way for nanotechnology, the science of semiconductor, molecular biology and many other scientific disciplines.
In the 1980s, we can not see atoms then German physicists Gerd Binnig and Heinrich Rohrer uses a quantum phenomenon in which atoms escaped from the surface of a solid, form a sort of cloud hanging over the surface. By moving the tip of a metal on the surface at a distance very, very small, overlapping atomic clouds produce an atomic exchange.
The atomic exchange produces a very small amount of electric current to flow between the tip and the surface. This electric current can be measured. It is through these current variations that STM provides information on the structure and topography of the surface. Then from this information, a three-dimensional model at the atomic scale is constructed which gives an image of the sample surface. Thus we can see today, this new quantum world and represent the structure of matter in the infinitely small. For this invention, Gerd Binnig and Heinrich Rohrer get the Nobel Prize for Physics in 1986.


The scanning tunneling microscope has preceded all other scanning probe microscopes, more modern, such as atomic force microscope (AFM) and near-field optical microscope.
This type of scanning probe microscopes has enabled the development of nanotechnology which need to manipulate objects of nanometric size (less than the wavelength of visible light from 400 to 800 nm).
The scanning tunneling microscope illustrates vividly, quantum mechanics by measuring the "enclosure quantum."
The enclosure quantum images show analogy between the matter waves associated with electrons and waves on the surface of the water (image above).
The scanning tunneling microscopy requires the use of a sample conductor of electricity but if the sample is insulating, using a technique similar to the atomic force microscopy (AFM Atomic Force Microscope).
Today, amorphous materials, non-crystalline, are observed by atomic force microscopy.

 AFM atomic force microscope

Image: The scanning tunneling microscopy requires the use of a sample of material, conductor of electricity, but if the sample is an insulator, then used the atomic force microscopy. Omicron VT-AFM XA (AFM Atomic Force Microscope - STM Scanning Tunneling Microscope)

Tunneling effect


We now come to the tunnel effect. At any wave is associated a particle, is called the wave-particle duality. In classical physics, the particle can not escape its nucleus, if its kinetic energy is greater than the potential energy of its link with the nucleus. For an electron to pass the limit is the potential energy of the link, that is the electromagnetic force which keeps it in its enclosure. For the proton, the cross is limited to the potential energy of its link, i.e. the strong nuclear force that keeps sticking to other nucleons. In quantum physics, it happens otherwise, the particle is represented by its wave and this wave is not completely captive inside the enclosure around the nucleus, it can go to the other side of the barrier of the potential even if its kinetic energy is less than the potential energy. Of course the probability of escape from the nucleus is extremely small, but it exists. Moreover, this property of quantum mechanics explains the disintegration of matter. Everything happens as if the wave digging a 'tunnel' through the barrier of potential to move across on the other side of the slope, and released from the electromagnetic or nuclear glue, electrostatic repulsion takes over, this is known as the tunnel effect of quantum mechanics. Thus the electron can pass through the vacuum of the atom, leaving the metal that contains it and reach another conductive metal. But the image of the quantum transition is more subtle, it is comparable to the image of a ghost passing through a wall. A part of proton or electron cloud pass the barrier of the potential while the other remains in the atom 'halved' the cloud will recover on one side or the other, as if there was a nano tunnel. Proton and the electron cloud will therefore pass or not according to its kinetic energy. In summary, more the barrier of the potential is high more the thickness to cross is large and more the nucleus 'long-lived'.


Indeed, this explains the half-life times of isotopes (see note below). The half-life times are very long for some isotopes of chemical elements, such as uranium-238 (4.5 billion years), uranium-234 (240 000 years) or radium 226 (1600 years). For cons, the intense radioactivity of radon shortens its half-life, it is 3.8 days for radon-222 used in radiotherapy. If we represent by a diagram, the potential energy of a particle, like the electron or the proton bound to a nucleus, one can imagine a hill much lower than it away the center of attraction. We deduce that more the radioactivity is strong, less the tunnel to dig will be long (picture opposite). But the wave did not stop at a particular point, it spreads into the barrier, although its amplitude decreases rapidly if the potential barrier is very thin, the wave passes through like a ghost and spreads to the next point of attraction. This is a direct consequence of the probabilistic nature of the wave associated with the evolution of a quantum particle, because even if the wave function of the particle through the barrier weakened, there is a nonzero probability to pass there through.

NB: the half-life is the period radioactive. This is the time required for half of the radioactive nuclei of an isotope decays to become a stable element.

Image: Wave representing a particle in the nucleus. The wave associated with the particle is not fully shown in the center of the nucleus but slightly overlaps the other side of the barrier of the potential with extremely small probability. More the barrier of the potential is high, more the thickness to across is great.  Wikipedia.

 illustration of the tunnelling effect

energy of a particle quantum tunneling

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