Ordered moments and relation to Radon transform of Wigner quasiprobability

It is shown that the symmetrically ordered moments of boson operators for a single boson mode can be reconstructed from the corresponding moments of t he Radon transform of the Wigner quasiprobability for discrete sets of equi distant inequivalent angles which solve the circle division problem. This r econstruction is sometimes simpler than the corresponding reconstruction of the normally ordered moments where one first has to multiply the Radon tra nsform with Hermite polynomials in comparison to power functions for symmet rically ordered moments and then to integrate. The connection to the recons truction for the general class of s-ordered moments is established. The tra nsition from discrete sets of angles to integration over angles via averagi ng over the discrete angles is made. The results are applied to displaced s queezed thermal states. It is shown how the ordered moments for these state s can be explicitly found from the calculated Radon transform of the Wigner quasiprobability. The obtained formulae for these moments possess independ ent interest since they contribute to the discussion of the properties of t he most general class of states with quasiprobabilities of Gaussian form wi th many possible special cases as, for example, squeezed coherent states an d squeezed thermal states.