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Abstract:
The problem of state determination of quantum systems by the probability distributions of some observables is considered. In particular, we review a question already asked by W. Pauli, namely, the determination of pure states of spinless particles by the distributions of position and momentum. In this context we give a new example of two wave functions differing by a piecewise constant phase having the same position and momentum distributions. ThePauli problem is investigated also under incorporation of special types of the Hamiltonian. Moreover, in case of spin-1 systems with three-dimensional Hilbert space, it is shown that the probabilities for the values of six suitably chosen spin components determine their state.
