A procedure is described that can be used to reconstruct the quantum state of a molecular ensemble from time-dependent internuclear probability density functions determined by time-resolved electron diffraction. The procedure makes use of established techniques for evaluating the density matrix and the phase-space joint probability density, that is, the Wigner function. A novel expression for describing electron diffraction intensities in terms of the Wigner function is presented. An approximate variant of the method, neglecting the off-diagonal elements of the density matrix, was tested by analyzing gas electron diffraction data for N2 in a Boltzmann distribution and TRED data obtained from the 193？nm photodissociation of CS2 to carbon monosulfide, CS, at 20, 40, and 120？ns after irradiation. The coherent changes in the nuclear subsystem by time-resolved electron diffraction method determine the fundamental transition from the standard kinetics to the dynamics of the phase trajectory of the molecule and the tomography of molecular quantum state. 1. Introduction In accordance with basic quantum principles, the state of an individual molecule cannot be determined experimentally [1]. However, for an ensemble of similarly prepared systems, it is possible to determine their state operator, the so-called density matrix. Knowing the state of a system means having the maximum possible information about all physical quantities of interest available [2]. The density matrix and the joint phase-space probability density, or Wigner function, [3, 4] have a one-to-one correspondence [5] that describes the maximal statistical information available. Thus, in the following text, when the term molecular quantum state is used, we mean the quantum state of an ensemble of similarly prepared molecular species. In 1933 it was demonstrated by Freenberg [6] (see also [1, page 71]) that, in principle, a pure quantum state can be reconstructed from the time-dependent coordinate probability density and its derivative . It was shown by Weigert [7] that a pure quantum state may also be reconstructed by measuring the distribution at time and monitoring its evolution after a short time interval ; that is, . For mixed quantum states, the method of optical homodyne tomography to measure the Wigner function (and density matrix) was first demonstrated by Smithey et al. [8, 9] for both vacuum and squeezed vacuum states of a single spatial-temporal mode in an applied electromagnetic field. (A number of investigations into the preparation and measurement of the quantum state of light may be
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