Through introducing an intermediate entangled state representation |β〉λν interpolating the entangled states |η〉 and |ξ〉, the eigenvalues and eigenvectors of a bipartite fully-coupled oscillators are discussed within some different situations.
The coherent entangled state |β, x〉 is proposed in Fock space, which exhibits both the properties of the coherent and entangled states. The |β, x〉 makes up a new quantum mechanical representation, and the completeness relation of |β, x〉 is proved by virtue of the technique of integral within an ordered product of operators. The corresponding Schmidt decomposition of |β, x〉 is investigated. Furthermore, a feasible experimental scheme of |β, x〉 is presented, and generalized P-representation is constructed in the coherent entangled state |β, x〉.