Global structure and geodesics for Koenigs superintegrable systems
Global structure and geodesics for Koenigs superintegrable systems
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Koenigs 超积系统的全局结构和测地线
DOI：
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发表时间：
2015
期刊：
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通讯作者：
G. Valent
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文献类型：
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作者：
G. Valent
我们提出了一个新的推导的局部结构的柯尼希斯度量使用的框架奠定了由Matveev和Shevchishin。所有这些动力系统允许一个潜在的保持其超可积性（SI），其中大多数被证明是全球定义在要么是E2或E2。由于它们的二次积分，它们的测地线流很容易确定。使用卡特（或最小）量子化，我们表明，形式SI是保持在量子水平和两个度量，其中所有的测地线是封闭的，它甚至可以计算经典的作用变量和量子哈密顿量的点谱。
We present a new derivation of the local structure of Koenigs metrics using a framework laid down by Matveev and Shevchishin. All of these dynamical systems allow for a potential preserving their superintegrability (SI) and most of them are shown to be globally defined on either ℝ2 or ℍ2. Their geodesic flows are easily determined thanks to their quadratic integrals. Using Carter (or minimal) quantization, we show that the formal SI is preserved at the quantum level and for two metrics, for which all of the geodesics are closed, it is even possible to compute the classical action variables and the point spectrum of the quantum Hamiltonian.