量子台球的升降算符
Raising and lowering operators for quantum billiards
摘要：
对于平面可积台球，本征态可以相对于由量子数确定的量进行分类。给定量子数为$m, n$，表示一个类的指数为$c = m\, \mbox{mod}\, k\,n$，表示自然数$k$。我们在这里表明，整个塔的状态可以产生从一个最初给定的状态，通过应用这里介绍的运营商。因此，这些算符在台球中的作用与角动量代数中的升降算符相同。
英文摘要：
For planar integrable billiards, the eigenstates can be classified with respect to a quantity determined by the quantum numbers. Given the quantum numbers as $m, n$, the index which represents a class is $c = m\, \mbox{mod}\, k\,n$ for a natural number, $k$. We show here that the entire tower of states can be generated from an initially given state by application of the operators introduced here. Thus, these operators play the same role for billiards as raising and lowering operators in angular momentum algebra.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
