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Using the projection evolution (PEv) approach, time can be included in quantum mechanics as an observable. Having the time operator, it is possible to explore the temporal structure of various quantum events. In the present paper, we discuss the possibility of constructing a quantum clock which advances in time during its quantum evolution, in each step having some probability to localize itself on the time axis in the new position. We propose a working two-state model as the simplest example of such a clock.
Góźdź et al. (Fri,) studied this question.