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

We construct four linear composite operators for a two-particle system and give common eigenvectors of those operators. The technique of integration within an ordered product (IWOP) of operators is employed to prove that those common eigenvectors are complete and orthonormal. Therefore, a new two-mode intermediate momentum-coordinate representation which involves quantum entanglement for a two-particle system is proposed and applied to some two-body dynamic problems. Moreover, the pure-state density matrix $\left| {\xi _1 ,\xi _2 } \right\rangle _{C,DC,D}\hs{-1mm}\left\langle {\xi _1 ,\xi _2 } \right|$ is a Radon transform of Wigner operator.