New relationship between quantum state’s tomogram and its wave function

Abstract

By searching for - and -ordering form of the coordinate-momentum intermediate representation (formed by the eigenvector of with eigenvalue being x, ), and noting that is just the Radon transformation of the Wigner operator, we find new relationship between a quantum state ’s tomogram and its wave function in coordinate (or momentum) representation, i.e. the tomogram can be split into two parts, one is ’s Gaussian integration transformation with the parameter and another is ’s Gaussian integration transformation with the parameter . In this way, the quantum tomogram of number state is conveniently deduced. We also derive Radon transform of and , which can be either viewed as - and -ordered operator correspondence of the classical function .