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Wigner function is a quasi-distribution that provides a representation of thestate of a quantum mechanical system in the phase space of position andmomentum. In this paper we find a relation between Wigner function andappropriate measurements involving the system position and momentum whichgeneralize the von Neumann model of measurement. We introduce two probescoupled successively in time to projectors associated with the system positionand momentum. We show that one can relate Wigner function to Kirkwood jointquasi-distribution of position and momentum, the latter, in turn, being aparticular case of successive measurements. We first consider the case of aquantum mechanical system described in a continuous Hilbert space, and thenturn to the case of a discrete, finite-dimensional Hilbert space.

Wigner function and the successive measurement of position and momentum