On the entangled state representation with continuum variables

We propose the conception of entangled state representation with continuum variables. We analyze the non-factorizable properties of the \eta] state, the common eigenvector of two-particle relative position and total momentum (Fan Hongyi and J.R. Klauder, Phys. Rev. A49 (1994) 704), and recast it into the standard form as the state prepared in a parametric down conversion process which involves the entanglement of idle and signal photons. We name the set of \eta] as entangled state representation, as it is orthonormal and complete.