论文标题
圆上的相干状态：Kummer函数和Zak转换的半经典矩阵元素
Coherent States on the Circle: Semiclassical Matrix Elements in the Context of Kummer Functions and the Zak transformation
论文作者
论文摘要
我们通过两种方式在文献中在文献中的圆圈上扩展了以前的结果。一方面，我们表明，可以通过Kummer的Confluent超几何函数来精确地分析动量运算符的分数能力的期望值。早些时候，这些期望值仅通过使用合适的估计来获得。另一方面，我们认为Zak变换不仅是映射谐波振荡器的相干状态，以使其在圆圈上进行的相干状态，而且还使用Zak变换的属性来得出矩阵元素之间相对于L2（R）和L2（R）和L2（S1）的相干状态之间的关系。这为圆上的连贯状态计算半经典矩阵元素提供了另一种方法。在某些方面，此方法简化了半经典计算，特别是如果一个人仅对经典限制感兴趣，即半经典扩展中的零订单项。
We extend former results for coherent states on the circle in the literature in two ways. On the one hand, we show that expectation values of fractional powers of momentum operators can be computed exactly analytically by means of Kummer's confluent hypergeometric functions. Earlier, these expectation values have only been obtained by using suitable estimates. On the other hand, we consider the Zak transformation not only to map harmonic oscillator coherent states to coherent states on the circle as it has been discussed before, but we also use the properties of the Zak transformation to derive a relation between matrix elements with respect to coherent states in L2(R) and L2(S1). This provides an alternative way for computing semiclassical matrix elements for coherent states on the circle. In certain aspects, this method simplifies the semiclassical computations in particular if one is only interested in the classical limit, that is the zeroth order term in the semiclassical expansion.
