Recapitulating Quantum Phase Space Representation by Virtue of Normally Ordered Gaussian Form of Wigner Operator
Fan Hong‐Yi, Xing-Lei Xu, Hongqi Li · Communications in Theoretical Physics · 2010
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.