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Exact wave solutions for particles with spin 0, 1/2 and 1 in the staticcoordinates of the de Sitter space-time model are examined in detail. Firstly,for a scalar particle, two pairs of linearly independent solutions arespecified explicitly: running and standing waves. A known algorithm forcalculation of the reflection coefficient $R_{\epsilon j}$ on the background ofthe de Sitter space-time model is analyzed. It is shown that the determinationof R_{\epsilon j} requires an additional constrain on quantum numbers \epsilon\rho / \hbar c >> j, where \rho is a curvature radius. When taken into accountof this condition, the R_{\epsilon j} vanishes identically. It is claimed thatthe calculation of the reflection coefficient R_{\epsilon j} is not required atall because there is no barrier in an effective potential curve on thebackground of the de Sitter space-time. The same conclusion holds for arbitraryparticles with higher spins, it is demonstrated explicitly with the help ofexact solutions for electromagnetic and Dirac fields.

On exact solutions for quantum particles with spin S= 0, 1/2, 1 and de Sitter event horizon