Abstract
The paper considers the problem of finding the joint probability distribution of position, P(q 0,q 1,…, qN ), at the different times t 0,t 1, …, tN . The problem is addressed both classically and quantum mechanically. The characteristic function approach is used and it is shown that for certain cases the quantum mechanical answer is the same as the classical answer with replacement of the initial classical probability distribution by the Wigner distribution of the initial wave function. This is the case for taking a certain form of the quantum characteristic function. Other choices are also discussed.
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