Using the normally ordered Gaussian form of the Wigner operator we recapitulate the quantum phase space representation, we derive a new formula for searching for the classical correspondence of quantum mechanical operators; we also show that if there exists the eigenvector |q⟩_λ,ν of linear combination of the coordinate and momentum operator, (λQ + νP), where λ, ν are real numbers, and |q⟩_λν is complete, then the projector |q⟩_λν⟨q| must be the Radon transform of Wigner operator. This approach seems concise and physical appealing.