Stackel系统的平坦极小量子化与量子可分性
Flat minimal quantizations of Stackel systems and quantum separability
摘要：
本文研究了经典Stäckel系统的量子化问题和相关量子哈密顿量的可分性问题。首先，利用Stäckel变换的概念，所有考虑的系统表示为相关的欧几里德位形空间的平坦坐标。然后，应用所谓的平坦最小量化过程，以便在相应的希尔伯特空间中构造适当的埃尔米特算子。最后，我们区分了一类Stäckel系统，它仍然是可分的后，任何允许的平坦极小量子化。
英文摘要：
In this paper, we consider the problem of quantization of classical Stäckel systems and the problem of separability of related quantum Hamiltonians. First, using the concept of Stäckel transform, all considered systems are expressed by flat coordinates of related Euclidean configuration space. Then, the so-called flat minimal quantization procedure is applied in order to construct an appropriate Hermitian operator in the respective Hilbert space. Finally, we distinguish a class of Stäckel systems which remains separable after any of admissible flat minimal quantizations.
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