Abstract
Based on the reference [1] , the mathematical and quantum statistical properties of the orthonormalized eigenstates of operator αk (k=3) are studied in this paper. It is found that all the orthonormalized eigenstates have nonclassical effects and they form a nonclassical complete representation. The result given by the reference [1] in the case k = 3 is only a special instance of the general conclusion of ours.

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