New two-mode intermediate momentum-coordinate representation with quantum entanglement and its application

We construct four linear composite operators for a two-particlesystem and give common eigenvectors of those operators. Thetechnique of integration within an ordered product (IWOP) ofoperators is employed to prove that those common eigenvectors arecomplete and orthonormal. Therefore, a new two-mode intermediatemomentum-coordinate representation which involves quantumentanglement for a two-particle system is proposed and applied tosome two-body dynamic problems. Moreover, the pure-state densitymatrix $left| {xi _1 ,xi _2 } rightrangle _{C,DC,D}hs{-1mm}leftlangle {xi _1 ,xi _2 } right|$ is a Radontransform of Wigner operator.