To do this, the Fourier variable separation method will be used, with respect to solving an equation of the form (4), the form of the function (5) will be adopted, where, after substitution, the form (6) is formed, from which 2 separate ordinary differential equations are derived.

The equation is solved in time to the state of the general form, according to (7), but due to the presence of initial conditions in (3), the present form can be solved by means of representation in the form of a system (8), taking into account the finding of the formula-dependence on the independent variables of the general form of the function (9), where after solving the formed equation after substituting the formula of the independent variable, the form of the introduced constant (10) in (6) is formed.

The value of the constant makes it possible to determine the value of the first and, accordingly, the opposite of the second independent constant (11), which, after substituting into the general form of the time function (7), gives its private emerging form (12) and (Fig. 1).

Fig. 1. Graph of the function

To continue the study, after establishing the actual form of the function in time, it is necessary to solve the formed ordinary differential equation with respect to the coordinate, which was obtained in the ratio (6). Since the value for the constant was also obtained in (10), after substitution, a final form of an ordinary differential equation in coordinate is formed, for which there is a constant from the characteristic of the form (13), and then the general form of the function (14).

When forming the problem, boundary conditions were also indicated, the substitution of which allows us to operate from the conclusions of the expression for the third and also opposite, as can be seen from the boundary conditions, independent constant, which in this case has a large-scale appearance, for which a replacement is introduced (15).

Substituting the resulting replacement allows you to ultimately form a simplified view of the function at the coordinate (16).

The result of the study is the assembled form of the function of the quantum mechanical state of the tunneling system. However, in this case, the desired function is initially a probability distribution function, for which only the square of its module has physical meaning. Based on this, it is possible to form the form of the square of the module of the function, as for the boundary conditions to be set, for the reason that initially the problem required complete preservation of information and in the case of data transition to an imaginary space, the boundary conditions were set to the original form of the function, for which the square of the module is represented in (17—18).

Thus, a full-fledged pattern was derived that predicts the probability distribution of finding a response signal for a given case at the maximum distance from the Earth for the probe.

According to the results of the study, a function depending on 2 variables was obtained, which can be constructed and according to the initial projection, the first graph of the function is formed without an additional power factor. After applying the appropriate processing (18), the function remains the same, but its parameters describe the actual picture (Fig. 2).

Fig. 2. Graph of the probability distribution of finding a signal beam

So, from Figure 2 it is clearly seen that as time passes along the numerical axis in increments of 2.35022802 seconds-meters to 70.51 seconds-meters or along the ordinary axis in increments of the same amount of meters to 30.55296 meters of range, it is possible to state the probability of finding a beam at 11.27337%, which makes it possible to assert, based on The parameter of 70.51 seconds is meters or 21,137,419,062 meters in the usual metric coordinate system, which means that the beam is likely to be found near the Earth and the signal can be received accordingly.