  We employ the method of comparison equations to study the propagation of a
massless minimally coupled scalar field on the Schwarzschild background. In
particular, we show that this method allows us to obtain explicit approximate
expressions for the radial modes with energy below the peak of the effective
potential which are fairly accurate over the whole region outside the horizon.
This case can be of particular interest, for example, for the problem of black
hole evaporation.
