Negative Effects Of Selling Stock

The development of quantum mechanics makes possible the discovery of new effects, impossible from a classical viewpoint. Perhaps the most popular is the tunnel, where making a quick comparison and bad, it's like throwing a ball at a wall to cross it without touching it. This is how it appears from an analysis of a similar situation, through the Schrödinger equation .

quantum Wall

Consider first what is meant by " wall" and what happens to an electron when it arrives. The energy of a particle is always the sum of its kinetic energy and potential energy. Thus, energy will always be equal to or greater than the potential. The cases in which the energy is lower than potential from classical physics, states represent unattainable by a particle. Thus, the point at which the total energy equals the potential represents a "turning point , the particle can not move forward, but must go back. Is the equivalent of a "wall ."

In the figure, the electron energy above is greater than the step, and both are superior, losing a bit of kinetic energy. Below the electron instead he should go back after reaching the point where its energy is equal to the potential energy, and therefore its kinetic energy is zero at that point.

Consider the situation of the second electron from the quantum point of view, with the Schrödinger equation.

The equation to solve is:

whose solution we saw in the previous entry , is a combination of sine and cosine. The combination of sine and cosine, by Euler's formula is equivalent to an exponential function imaginary and more useful for the analysis that follows. Thus, the wave function can be expressed generally as:

As we saw earlier, k (the wave vector ) is related to the angular momentum and therefore the sense that the particle moves. A + means that moves in the direction of x increasing (going from left to right). The sign - describes a movement in the opposite direction. As the picture has been raised, we are in the first case, ie, the electron moves from left to right, whereas in the wave function describes the first term ( k positive). Therefore, in our case, you should choose B = 0 to cancel the second term.

Let's see the two regions of space that defines the step. On the left, (EV) is a positive quantity (total energy greater than the potential), and the wave equation represents a free electron (an imaginary exponential, or a combination of sine and cosine). In contrast, in the right area, (EV) is negative (energy less than the potential energy), the wave vector is imaginary , and the wave function represents a real exponentially decreasing. That is, although it is a forbidden zone as classical physics, in quantum mechanics a particle can exist in that area, but with a diminishing likelihood as deeply into the wall.

The distance that an electron can penetrate into the forbidden zone before your chance is almost nil, depends on the difference between energy and the value of the potential. The greater the difference EV, the probability falls more rapidly. In the extreme case in which V tends to infinity, the penetration depth tends to zero, ie, the electron does not enter into the wall (as we assumed when we spoke of quantum well).

The tunnel effect

Therefore, a particle can penetrate a wall of potential, something impossible according to classical physics. A particle can penetrate a distance (small), although the probability of finding the particle at that location decreases as depth. What if the potential wall finishes before this probability is terminated, or reduced too?. In this case, the "other side " from the wall of the wave function again described by a free electron. It is therefore possible that an electron reaches a barrier, the cross, and appears on the other side of it, with a certain probability, although less than it did before crossing the barrier.

The probability of crossing the barrier depends on the mass of the particle, the barrier height, but above all, of its width. The typical distances that probability is sufficient to tunnel is in the order of angstroms and nanometers. Alpha decay



The emission of alpha particles is related to the tunnel effect. An alpha particle is an atom composed of 2 protons and 2 neutrons, not electrons. Corresponds to a nucleus of helium 4 (4 ^I 2 +). An atom with a large number of protons and neutrons keeps these particles stuck together by the strong interaction. An outline of the potential energy inside an atom is as follows:

There is an area of \u200b\u200bpotential barrier at the transition between the strong interaction domain and the electrostatics. Overcoming this barrier would require making a lot of energy. However, an alpha particle is able to cross the barrier by tunnel effect, breaking up the nucleus to which it belonged.

The scanning tunneling microscope

The tunnel is now the basis of some devices such as diodes, lasers and detectors. But one of the most important is related to the surface microscopy.

View STM: Scanning tunneling microscope

Implantation Thick White Mucus

The STM tunneling: The scanning tunneling microscope

The scanning tunneling microscope (Scanning Tunneling Microscope) was invented in 1981 by Gerg Binnig and Heinrich Rohrer. Received the Nobel Prize for it in 1986. The STM uses the ability of electrons to traverse a potential barrier to record the electrical current that occurs between a tip (or probe), and the sample. An electron in a metal has a particular energy. The solid surface represents a potential barrier to be " jump" to get out of it. By bringing the metal (the probe), and applying an electric field to direct the electron to the metal, it creates a barrier with a distance small enough for the electron tunneling can be no need to jump the barrier.

The current can be recorded with an ammeter is proportional to the probability that the tunnel occurs. Which in turn depends on the distance between the tip and sample. In this way, recording the electrical current, information is obtained the distance that the tip is.

A simple schematic of an assembly of a STM tip is near a sample records the intensity tunnel occurs. The intensity controls a piezoelectric (material that varies in length by applying an electric field) acting on the tip to zoom in or removed from the sample, which is mounted on a table x, and the moves. Thus, to take a trip on y, the tip scans the sample, recording the intensity that occurs at each point.

There are several ways of operating in a VTS, but the most common is to maintain a constant tunneling current. This is achieved by maintaining distance between tip and sample constant. As the tip scans the sample in the x-axis and and , will control the tunneling current. When the tip reaches a point where the sample has valleys and outgoing, this current will vary. This variation indicates that you zoom the tip of the sample in the z axis to return to get the same stream, which is done through the piezoelectric. One computer had to be recorded as pan and zoom the point on the axis z , at that point ( x, y ) of the sample, so that after completing the sweep has a map that shows the variations in z axis. Ie a graph is related to the topography, the shape of the sample.

Another way to act is to maintain constant tip position, and record the power at each sample point, which varies as it passes through valleys and outgoing. However, there is a risk of crashing the tip into a projection of the sample, spoiling both the one and other. The end result also gives information on the topography of the sample.

Usually, the results are presented in map form x, y colors where the color code represents the z-axis values \u200b\u200b .

microscope Act, allowing " see "the surface of the sample. The accuracy of this instrument is that it can see the atoms of a solid. It is useful to study the surfaces of solids and their electronic properties. However, samples must be conductive. Another requirement for the STM is to be run dry, leading to integrate the system into vacuum chambers, with the hassle to change samples involved.

To see some images obtained by STM , you can do in the website nanotechnology.

View tunneling The