GENERATION OF ORTHONORMALIZED EIGENSTATES OF THE OPERATOR-A(K) (FOR K GREATER-THAN-OR-EQUAL-TO 3) FROM COHERENT STATES AND THEIR HIGHER-ORDER SQUEEZING

In this paper, we study first the connection of the k orthonormalized eigenstates of a(k) with coherent states, then, according to the higher-order squeezing defined by Zhang et al. [Phys. Lett. A 150, 27 (1990)], study the properties of the higher-order squeezing of k orthonormalized eigenstates. Our results show that the k orthonormalized eigenstates can be represented as a linear superposition of k coherent states, and that all of them are minimum uncertainty states of the operators Z1(N) and Z2(N) (N = mk, m = 1, 2,3,... ) for even and odd k, and all of them have the Nth-order squeezing [N=(m + 1/2)k, m = 0,1,2,... ] for even k.