Introduction We discuss the situation where the potential energy of the system is finite at infinity (hereafter it is zero), then particles can appear at infinity, and the wave function is not zero at infinity, because there is no wave function at infinity Constraints, the energy of the system can be any value, which constitutes a continuous spectrum. This kind of problem belongs to the problem that the particles are scattered by the potential field. The particles come from infinity, and are scattered by the potential field and then go to infinity. Consider the particles moving in a one-dimensional space barrier, the potential energy goes in the region of the finite region (CKxa). The phenomenon that particles can still penetrate the barrier when the energy E is less than the barrier height is called tunneling.
The probability flow density of the incident wave is the transmitted wave probability flow density is the reflected wave probability flow density is C. It may cross the barrier and 1 may be reflected back; the energy Allrigh transmitted wave. Probability of flow density: degree and entry. The ratio of jet probability current density to physical and engineering Vol. Is called the transmission coefficient, which is represented by D, the same is true for D 12, and the reflection coefficient means that part of the incident particle penetrates to the right of the potential barrier and part of it reflects back.
= ik3, replace k2 with ik3, the previous calculation still holds. It can be concluded that because ki and k3 are of the same order, when k3a1, the above formula can be written as D = Doexp (−2k3a). The transmission coefficient decreases with the widening or heightening of the barrier.
The tunnel effect and tunnel current theory in quantum mechanics came into being shortly after STM came out, and theoretical articles about it came into being, but most of them are based on Bardeen tunnel current theory. The tunnel current formula is 1994-2015 ChinaS graphite as the material for experimental observation and analysis! Stone and spherical function We quantify the size of the radial function and simulate the spherical function, and we can obtain the atomic theory model of carbon atoms. When discussing the electronic cloud, we must first clarify that the electronic cloud does not actually have electrons, but to measure the possibility of the existence of electrons. For this, we have to measure it multiple times in time and times. The electron movement is extremely fast, that is, the scanning time of our probe is long enough so that the electron moves to the edge with a high probability-here the barrier is small, and the penetration efficiency increases.
Observing the cross-section of the image under the constant current mode on the graphite surface, we can find a common law: their image fluctuations show a certain trend. This is found in a large number of experimental cross-sections. We can think of this as an electron cloud distribution of atomic structure.
Comparing our theoretical analysis above, we can find that the above graph and theoretical results can be qualitatively compared. We know quantum, but we can analyze this result qualitatively. The tunnel current display is actually a supplement to the electrons of the electron cloud. The necessary condition for forming the tunnel current is that the tunnel electrons contact the graphite electron cloud. In other words, we can use the size of the electron tunnel current to describe the shape of the atomic electron cloud.
The electronic structure of graphite is mainly determined by the delocalized X electrons between layers, so the interaction between layers has a great influence on the electronic state of graphite near the Fermi surface. In the graphite monolayer, the carbon-carbon bond length is 1.45A, the lattice constant in the plane is 2.456A, and the graphite layer spacing is 3.35A. The graphite layer is combined into layered crystals in the form of ABAB, such as (1), Among them, B is displaced by 1.45A relative to the layer A along a triple symmetry direction. This displacement breaks the hexagonal symmetry of the graphite monolayer, resulting in two atoms in different positions, one is an atom, directly in Above, the other is a P atom, in the middle of the carbon six ring of the next layer, which is a vacancy. The atoms of graphite constitute a hexagonal lattice, while in the STM diagram, the atoms constitute a digonal lattice, such as (2), so only one of the a and P atoms can be seen. Theoretical calculations show that due to the interaction between layers, the electronic state density of p atoms is much larger than that of a atoms in the energy range detected by STM, so the accepted view is that only n atoms can be seen. In some, a atom is called A atom, and P atom is called B atom. The spacing of P atoms in the STM diagram is 2.45A. This distance is often used to calibrate the lateral distance of the STM diagram, while the height of 3.35A single step is often used to calibrate the longitudinal distance.
The electrons in the metal are not completely confined to the metal surface, and the electron cloud density does not suddenly change to zero at the surface boundary; outside the metal surface, the electron cloud density decays exponentially, and the attenuation length is about 1 nm. The copper atom scale is 0 .1nm, the attenuation length is much larger than the atomic scale, so that we can only see the effect of multiple atoms, such as.
The scale of the cluster can be clearly seen in the metal surface structure is very complex, many metals in order to achieve the lowest energy, (channel) function (number) and its hybridization characteristics, but the tunnel spectrum measurement only observed S, P energy The bands and F bands cannot contribute to the scanning tunneling spectrum measurement due to their electron hollow localization and centrifugal barrier.
Conclusion The comparison between the atomic structure diagram obtained by theoretical analysis and the experimentally measured diagram can be found to be consistent with our simulation analysis of the electron cloud theory, thus experimentally proving that the quantum mechanics model of the atomic electron cloud structure is correct, At the same time, the structure measured by the experiment is analyzed as a result of a combination of external factors.
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