Application of new entangled state representation to a two-coupled oscillator system

We study the eigenstate problem of a two-coupled oscillator system. A new entangled state representation \left\vert \gamma \right\rangle composed of the common eigenvectors of operators % (x_1+p_2) and (p_1+x_2) is established. Eigenvalues and eigenvectors of the Hamiltonian are obtained in \left\vert \gamma \right\rangle representations. The same problem is studied in the second-quantization representation. We find that the second-quantization representation can be used to derive the normally ordered product expression of eigenvector in Fock space. In particular, we find that the ground state of the Hamiltonian is a kind of generalized two-mode squeezed state.