Nonclassical properties of even and odd generalized coherent states for an isotonic oscillator

We used the numerical method to study nonclassical properties of the even and odd generalized coherent states and superposition states of generalized coherent states for an isotonic oscillator. The following was shown. (1) The quantum statistical properties of the even and odd generalized coherent states are very different from those of the usual even and odd coherent states, and the Nth-order (N = 2m + 1, m = 0, 1, 2,...) squeezing and sub-Poisson distribution appear alternately for both the even and odd generalized coherent states in some ranges of z = \beta\(2) The weaker the isotonic oscillator potential, the narrower the ranges. (2) The superposition states of generalized coherent states may exhibit the Nth-order squeezing effect too, and this kind of higher-order squeezing effect appears periodically.