论文标题
2：1振荡器的非线性梯子操作员和相干状态
Non-linear ladder operators and coherent states for the 2:1 oscillator
论文作者
论文摘要
考虑2：1二维各向异性量子谐波振荡器，并通过使用非兼容性二项式定理以及求解复发关系来定义新的状态集。生成的状态是$ \ mathfrak {su}（2）$二维各向同性振荡器的$ \ mathfrak {su}（2）的良好候选者。二维非线性通用阶梯运算符导致以非微不足道方式连接的几个状态链。计算了定义状态链的不确定性关系，发现他们承认了与经典2：1振荡器相应地产生波功能的身份和空间分布的分辨率。
The 2:1 two-dimensional anisotropic quantum harmonic oscillator is considered and new sets of states are defined by means of normal-ordering non-linear operators through the use of non-commutative binomial theorems as well as solving recurrence relations. The states generated are good candidates for the natural generalisation of the $\mathfrak{su}(2)$ coherent states of the two-dimensional isotropic oscillator. The two-dimensional non-linear generalised ladder operators lead to several chains of states which are connected in a non trivial way. The uncertainty relations of the defining chain of states are calculated and it is found that they admit a resolution of the identity and the spatial distribution of the wavefunction produces Lissajous figures in correspondence with the classical 2:1 oscillator.
