  Two measurable characteristics of microwave one-mode photon states are
discussed: a rotated quadrature distribution (tomogram) and
normally/antinormally ordered moments of photon creation and annihilation
operators. Extraction of these characteristics from amplified microwave signal
is presented. Relations between the tomogram and the moments are found and can
be used as a cross check of experiments. Formalism of the ordered moments is
developed. The state purity and generalized uncertainty relations are
considered in terms of moments. Unitary and non-unitary time evolution of
moments is obtained in the form of linear differential equations in contrast to
partial differential equations for quasidistributions. Time evolution is
specified for the cases of a harmonic oscillator and a damped harmonic
oscillator, which describe noiseless and decoherence processes, respectively.
