On phase instability in the case of scattering by a random potential

A study is made of a nonrelativistic model problem of the stability of phase functions in the case of scattering of a particle by a random time-independent potential. It is shown that the phase functions may be either stable or unstable depending on the parameters of the problem; a criterion is given for the changeover from stable to unstable conditions. In the latter case, the Usual quantum-mechanical treatment is incorrect and one must introduce an additional averaging procedure. This is a necessary sign of the statistical nature of the system. The instability criterion obtained is used in a discussion of the properties of intermediate compound systems that arise in the interaction of hadrons with nuclei and with one another.