非简谐振子湮没算符高次幂的本征态及其高阶压缩性质

Eigenstates of the Higher Powers of Annihilation Operator of a Non-Harmonic Oscillator and Their Higher-Order Squeezing

构造出了非简谐振子湮没算符 N次幂 (N≥ 3)的 N正交归一本征态 ,并且研究了它们的数学性质及其高次方压缩特性。其结果表明 ,它们能组成一个完备的希尔伯特 (Hilbert)空间 ;且当 N为偶数时 ,这些本征态均可呈现 M次方压缩效应 [M =(n +12 ) N ,n =0 ,1,2 ,… ]

The eigenstates of the Nth powers (N≥ 3) of the annihilation operator of the non- harmonic oscillator are constructed,and their mathematical and higher- order squeezing properties are studied.The results show that they form a complete Hilbertspace,and the Mthpower[M =(n +1 2 ) N;n =0 ,1, 2 ,… ] squeezing effects existin all eigenstates when Nis even.