  Two methodological troubles of the quantum theory of collisions are
considered. The first is the undesirable interference of the incident and
scattered waves in the stationary approach to scattering. The second concerns
the nonstationary approach to the theory of collisions of the type $a+b\to
c+d$. In order to calculate the cross section one uses the matrix element
$<cd|S|ab>$ of the $S$-matrix. The element is proportional to $\delta$-function
expressing the energy conservation. The corresponding probability $|<
cd|S|ab>|^2$ contains $\delta^2$ which is mathematically senseless. The known
regular way to overcome the difficulty seems to be unsatisfactory. In this
paper, both the troubles are resolved using wave packets of incident particles.
