The eigenvector set of |φ (x, r₁ , r₂)> with three compatible operators ( x^₁+x^₂+x^₃,p^₂ + p^₃ - p^₁ and p^₃ - p^₂) is constructed by virtue of Radon transformation of the Wigner operator and the technique of integration within an ordered product (IWOP) of operators. Its entanglement property is then revealed by deriving its standard Schmidt decomposition.|φ (x, r₁ , r₂)> makes up a new quantum mechanical representation. A new three-mode squeezing operator is found by using this entangled state representation.