q－玻色湮没算符高次幂的本征态及其性质

Eigenstates of Higher Power (k≥3) of the q-Boson Annihilation Operator and Their Properties

研究ｑ－玻色湮没算符高次幂（ｋ≥３）的正交归一本征态的数学结构，在此基础上讨论了它们的数学性质及其ｑ－压缩和振幅Ｎ次方压缩特性．发现它们能组成一个完备的希尔伯特（Ｈｉｌｂｅｒｔ）空间；且当ｋ为偶数时，这些本征态均可存在振幅Ｎ次方压缩．

In this paper, the mathematical structure of k orthonormalized eigenstutds of the higher powers (k≥3) of the q-boson annihilation operator are studied. Based on the work, the properties of the mathematics, q-squeezing and the amplitude N th-power squeezing are investigated. It is found that they form a complete q-Hilbert sauce, and the amplitude N th-power squeezing [N = (m + 1 /2)k, m = 0, 1, 2, ...] can exist in the all of them when k is even.