Все науки. №7, 2024. Международный научный журнал - страница 15

And also, based on the height of the potential barrier, it is possible to determine the boundary and initial conditions for the state function of the quantum mechanical system in (3).

The boundary conditions are formed from several statements. For use, such a system is necessary in which the probability of finding the beam after sending it in the radiator should be zero, at the specified target – on the Ground, should be equal to 100 percent. Despite the fact that with classical propagation at a time, taking into account such distance measurement, it is necessary that after 21,157,80283 seconds-meters, the probability of finding the beam on Earth was 100% and zero when reaching the Sun at 21,656,80762 seconds-meters. Based on the obtained indicators with respect to one dimension and time, equation (1) can be solved with the specified boundary conditions (3).

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).