By Professor Crispin W. Gardiner Ph. D (auth.)

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At the end of the experiment we have no apple, but consider the information gained to be relevant to similarly prepared apples, which others may choose to eat. Classical sampling theory does not normally take into account that sampling may destroy the sample, even though it is obvious that such destructive sampling is very common. It is conventional to say that these measurements are measurements of the second kind. In quantum mechanics we can conceptualise such a measurement very similariYAto the way we have already done.

The Hamiltonian evolution continues until the next measurement and so on. Eventually we obtain the multi time joint probability for obtaining a sequence of measured values corresponding to the measurements carried out sequentially. We will be able to show that by means of such a process we can, in principle, measure any time ordered correlation function of any quantum mechanical operators. 1 Sequences of Measurements Let us, for simplicity, consider the process of carrying out a sequence of measurements on a well defined initial quantum state l"p, to }.

12) 28 2. 11) : LHS; Refers to the situation before measurement. P(a; ii) = (probability that the system is in state a before measurement) x (probability of getting the value ii given that it was in the state a before measurement) RHS; P(a; ii) = Refers to the situation after measurement. 14) which means, in words, Probability the system is in the state la), given that the result ii has been measured ex: Probability that the system was in state la) before measurement x probability that the result is ii given that the state is la).

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