$q$振子的算子
Operators of the $q$-oscillator
摘要：
我们仔细研究了将\cite{ccr}的结果推广到$q$实q变形振子的可能性;为此，我们尽可能地利用变形参数的整个范围。我们分裂成两个取决于对易关系的解决方案是否有界或没有的情况。我们的{ \it主基序}是{ \it次正态}。变形参数$q$被重塑，这是使我们的方法有效的。新到达的参数，运营商$C$，有两个显着的性质：它分离的对易关系的湮灭和创造运营商的变形，以及它的$q$ -与这两个交换。这就是为什么引入操作符$C$似乎意义深远的原因。
英文摘要：
We scrutinize the possibility of extending the result of \cite{ccr} to the case of q-deformed oscillator for $q$ real; for this we exploit the whole range of the deformation parameter as much as possible. We split the case into two depending on whether a solution of the commutation relation is bounded or not. Our {\it leitmotif} is {\it subnormality}. The deformation parameter $q$ is reshaped and this is what makes our approach effective. The newly arrived parameter, the operator $C$, has two remarkable properties: it separates in the commutation relation the annihilation and creation operators from the deformation as well as it $q$-commutes with those two. This is why introducing the operator $C$ seems to be far-reaching.
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。
