On quantum description of motion with friction

AЁmethod of quantum description of motion in a dissipative system is considered. One-dimensional problem is described by a nonlinear integro-differential generalization of the Schrödinger equation. The case of free motion with friction is solved exactly. The problem with the infinite-wall potential is considered and an approximate solution is obtained. The solution provides an example of a system with friction with time dependent parameters, expired from the moment of its production. This effect can be tentatively applied for an interpretation of experimental indications on a time dependence of hadron effective cross-sections.