论文标题
在坐标的符号转化下的量子机械可观察物
Quantum Mechanical Observables under a Symplectic Transformation of Coordinates
论文作者
论文摘要
我们考虑在具有构二维系统的量化版本中，具有构型尺寸的量子机械可观察力的一般符号转换（也称为线性规范变换），其配置空间同构为$ \ Mathbb {r}^{q} $。使用索具希尔伯特空间的形式主义，我们为所有可观察物进行了特征状态。然后，我们确定这些本征态相应转换的明确形式。本文结尾包括一些例子。
We consider a general symplectic transformation (also known as linear canonical transformation) of quantum-mechanical observables in a quantized version of a finite-dimensional system with configuration space isomorphic to $ \mathbb{R}^{q} $. Using the formalism of rigged Hilbert spaces, we define eigenstates for all the observables. Then we work out the explicit form of the corresponding transformation of these eigenstates. A few examples are included at the end of the paper.
