  The model of weak measurements is applied to various problems, related to the
time problem in quantum mechanics. The review and generalization of the
theoretical analysis of the time problem in quantum mechanics based on the
concept of weak measurements are presented. A question of the time interval the
system spends in the specified state, when the final state of the system is
given, is raised. Using the concept of weak measurements the expression for
such time is obtained. The results are applied to the tunneling problem. A
procedure for the calculation of the asymptotic tunneling and reflection times
is proposed. Examples for delta-form and rectangular barrier illustrate the
obtained results. Using the concept of weak measurements the arrival time
probability distribution is defined by analogy with the classical mechanics.
The proposed procedure is suitable to the free particles and to particles
subjected to an external potential, as well. It is shown that such an approach
imposes an inherent limitation to the accuracy of the arrival time definition.
