Relations between scaling-transformed Husimi functions, Wigner functions and symplectic tomograms describing corresponding physical states

Abstract

Husimi Q-functions are the only functions from the class of Cohen quasi-distributions on phase space that after scaling transformation (q, p) - gt (lambda q, lambda p) remain in the same class when the modulus of the scaling parameter is smaller than unity and so, in this case, describe a physical state. We found the Wigner functions and symplectic tomograms of such states. We applied the obtained general results to the Fock states of the harmonic oscillator.