We construct the states that are invariant under the action of the generalized squeezing operator for arbitrary positive integer k. The states are given explicitly in the number representation. We find that for a given value of k there are k such states. We show that the states behave as n ^−k/4 when occupation number n → ∞ . This implies that for any k ≥ 3 the states are normalizable. For a given k, the expectation values of operators of the form are finite for positive integer j < (k/2 − 1) but diverge for integer j ≥ (k/2 − 1). For k = 3 we also give an explicit form of these states in the momentum representation in terms of Bessel functions.

我们为任意正整数k构造在广义压缩算子的作用下不变的状态。状态在数字表示中明确给出。我们发现对于给定的k值，有k 个这样的状态。我们表明，当职业数n → ∞时，状态表现为n ^{− k /4}。这意味着对于任何k ≥ 3，状态都是可归一化的。对于给定的k，形式运算符的期望值对于正整数j < ( k /2 − 1)是有限的，但对于整数j 是发散的≥ ( k /2 − 1)。对于k = 3，我们还根据贝塞尔函数在动量表示中给出了这些状态的明确形式。