We assume that, apart of the monitoring device, our system evolves under time evolution described by the Schrödinger equation with a self--adjoint Hamiltonian . We denote by the corresponding unitary propagator. Again, for simplicity, we will assume that does not depend explicitly on time.
Our second postulate reads: assuming that the monitoring started at time t=0, when the system was described by a Hilbert space vector , , and when the monitoring device was recording the logical value "no", the probability that the change will happen before time t is given by the formula:
Remark: The factor in the formula above is put here for consistency with the notation used in our previous papers.
It follows from the formula (1) that the probability that the counter will be triggered out in the time interval (t,t+dt), provided it was not triggered yet, is , where is given by
We remark that is the probability that
the detector will notice the particle at all. In general this number
representing the total efficiency of the detector (for a given initial
state) will be smaller than