论文标题
双层状态为该位置的广义特征和动量操作员
Bi-coherent states as generalized eigenstates of the position and the momentum operators
论文作者
论文摘要
在本文中，我们表明位置和衍生运算符，$ \ hat q $和$ \ hat d $，可以视为梯子操作员连接两个生物反对家族的各种向量，$ \ nathcal {f}_φ$和$ \ mathcal {f} f}_ψ$。特别是，$ \ Mathcal {f}_φ$中的向量本质上是$ x $，$ x^k $中的单个单元，而$ \ Mathcal {f}_ψ$中的向量是dirac Delta分布的弱衍生物，$δ^{（m）}（x）$，timess times times times times times timess一些普通化因素。我们还展示了如何为这些$ \ hat q $和$ \ hat d $构建双重状态，既可以作为$ \ nathcal {f}_φ$和$ \ Mathcal {f}_ψ$的收敛系列元素，或者使用两个不同的位移式操作员在框架框架的两个Vacua上使用两个不同的位移式操作员。我们的方法概括了普通连贯状态的众所周知的结果。
In this paper we show that the position and the derivative operators, $\hat q$ and $\hat D$, can be treated as ladder operators connecting the various vectors of two biorthonormal families, $\mathcal{F}_φ$ and $\mathcal{F}_ψ$. In particular, the vectors in $\mathcal{F}_φ$ are essentially monomials in $x$, $x^k$, while those in $\mathcal{F}_ψ$ are weak derivatives of the Dirac delta distribution, $δ^{(m)}(x)$, times some normalization factor. We also show how bi-coherent states can be constructed for these $\hat q$ and $\hat D$, both as convergent series of elements of $\mathcal{F}_φ$ and $\mathcal{F}_ψ$, or using two different displacement-like operators acting on the two vacua of the framework. Our approach generalizes well known results for ordinary coherent states.
