The phenomenon of the quantum tunneling effect is quite well-known and popular today. This effect itself is based on the fact that microparticles can overcome a certain potential barrier if its total energy, which remains unchanged and is not spent on overcoming the barrier, is less than the height of the barrier itself. Of course, such a phenomenon by definition could not occur on the scale of classical physics, at least because of its vivid contradiction, however, this effect itself is proven by numerous empirical results, since it underlies the most diverse phenomena of atomic, molecular physics, physics of the atomic nucleus and elementary particles, solid state and others.
For a better understanding of the present effect, we point out that let the definition of the kinetic energy of a particle be set initially according to (1), from which it can be seen that if the conditions of the quantum tunneling effect are met, it turns out that the momentum of such a particle satisfying the conditions set should become an imaginary quantity and it would seem that this could not be in reality, but together with this, the solution of the famous Schrodinger equation (2), where the potential energy of the particle is a constant, has a solution (3), from which the value for the momentum is derived as (4).
And although in this case the momentum becomes imaginary when the value of the potential barrier begins to exceed the total energy of the particle, as it was indicated. To understand the nature and causes of this phenomenon, you can resort to presenting a separate model with three potential barriers, for each of which your wave equations will be defined, after which the final expression will be derived, or you can use a more visual Heisenberg uncertainty relation. As can be seen from the first relation for inaccuracies of coordinates and momentum, with a more accurate determination of the coordinates of a particle, the accuracy of its momentum decreases, due to which we can talk about finding the magnitude of the momentum of particles in any suitable set of quantities at this time, which allows the particle to have a complex momentum value, which causes the tunnel effect. However, in this case, there will be a determination of the magnitude determining the probability of a particle passing through this barrier.
So the present transmission coefficient is determined according to the initial model, according to which let there be three potential barriers, the first and third of which have zero height, and the second is high enough to exceed the value of the total energy of the particle. In this case, during the approach of a particle to a potential barrier, the definition of its coordinate increases, due to which, according to the uncertainty ratio, the value of its momentum decreases, after which a certain number of its components can pass through the barrier, and a certain one can be reflected. It is the ratio of these two components that gives a certain definition of the probability current, where the probability current of the wave incident on the barrier acts as the numerator, and the probability current of the part of the wave passing through the barrier acts as the denominator. Also, the inverse value of this value is the reflection current, from where it is appropriate to determine their sum equal to one.
In addition, the value of these quantities, according to the laws of quantum mechanics, can be determined through a quasi-classical approximation, where the relations are determined according to (5).
In this case, we can say that if there is a particle with a certain energy value less than the value of the potential barrier, it also becomes possible to determine the probability with which this particle can pass through this potential barrier. So, for an electron with varying kinetic energy, to pass a potential barrier of 1 GeV, when its energy increases to this value, the probability function changes according to Graph 1.
In this case, it will be possible to visually observe how the probability of passage begins to change and already when the value becomes equal to the value of the potential barrier, even then it is no longer possible to talk about complete passage (6).
And although, on the one hand, the analysis of the present effect may be, in the original understanding, made to describe more well-known practical phenomena, but as it turned out, there are new methods according to which it is possible to transmit energy/information over an almost unlimited distance using this technology. The fact is that today it is possible to transfer to a particle a huge amount of energy up to tens of TeV, which is already equal to the value of a potential barrier consisting of 1,000 atoms standing in the way of the particle, that is, it can pass through a thousand atoms without expending energy with a probability of 64%, while initially giving a certain direction in space a real particle. And since the particle does not change its energy after passing the barrier, unless resources can be spent only as a means of overcoming probability, then we can talk about transferring the remaining amount of energy to a huge, cosmic distance.
So if the energy of 1 TeV becomes sufficient to overcome thousands of hydrogen atoms, with a diameter of 10—11 m, how can we say that this energy will be enough to overcome 10—8 m. It would seem that the distance is too small and the technology itself is not too cost – effective, but it is worth considering at least that such a method does not require the use of conductors and for transmitting, for example, energy to the ISS, the distance to which is estimated at a maximum point of 430 km, it is worth sending particles with energies of 4.3 * 1025 eV.
A value that becomes almost unrealistic given modern devices, but this definition is suitable if we take into account that the particle current will be measured in mA or MC, which can determine the charge through (7).
Where, from the available energy value, the velocity (8) can be calculated, but for a sufficient solution, it is necessary to initially decompose the resulting root with the transformation (9—10) into a Taylor series (11), from where it will be possible to obtain a percentage value.
Thus, it was possible to determine the approximation of the speed of light, which can be taken to be almost equal to the speed of light. And indicating that 1 micron is taken as the beam diameter, we can talk about the resulting charge value and the number of particles (12).
Therefore, we can say that it is possible to direct energy to a distance of 430 km in the amount of 4.3 * 1019 watts instantly, when the same value can be sent for 1.43 microseconds to the same distance, when acting with light radiation with the same power. And if, at such a relatively close distance, this method again does not seem to be cost-effective, then you can resort to the case when the distance is 1 light-year. Then it is worth resorting to a different definition.
Initially, it is worth pointing out that the density of matter in space is 3 * 10—28 kg/m3, which in turn is 2.9967* 1026 times less dense than the density of the estimated hydrogen, equal to 0.0899 kg/m3, from which we can say that with an already defined energy of 1025 eV, a particle can overcome in space as much the same distance or, by analogy, 1.288567 * 1029 km, which is 13,629,492,816,374.85 light-years, which is even more than the radius of the observable universe by 137,927.5 times.