Abstract: By the representation of the coordinate eigenvector ｜x〉 in the Fock space,the eigenvector ｜ψ〉 of the operator λx^＋μp^ is derived and its orthogonal relation is also proved.These results show that the eigenvector ｜ψ〉 satisfies the completeness and the orthogonal relations.Therefore,this eigenvector ｜ψ〉 can be qualified for a representation in quantum mechanics.When λ=1 and μ= 0,the eigenvector ｜ψ〉 evolves into the coordinate eigenvector ｜x〉;while λ=0 and μ =1,the ｜ψ〉 reduces to the momentum eigenvector ｜p〉.Therefore,the representation consisted by the eigenvectors ｜ψ〉 is an intermediate representation between the coordinate representation and the momentum representation.

Key words: Fock representation, normal ordering, coordinate-momentum intermediate representation