论文标题
谐波振荡器运动常数
Constants of Motion of the Harmonic Oscillator
论文作者
论文摘要
我们证明WEYL量化可以保留谐波振荡器的运动常数。我们还证明，如果$ f $是经典的运动常数，而$ \ mathfrak {op}（f）$是相应的运算符，则$ \ mathfrak {op}（f）$将schwartz类映射到本身中，并且定义了本质上定义了$ l^2（\ mathbb r r^n）$。结果，我们提供了$ \ mathfrak {op}（f）$的详细光谱信息。给出了谐波振荡器的经典运动常数的完整表征，我们还表明它们与Moyal产物形成代数。我们提供了一些有趣的例子，并在框架内分析了温斯坦的平均方法。
We prove that Weyl quantization preserves constant of motion of the Harmonic Oscillator. We also prove that if $f$ is a classical constant of motion and $\mathfrak{Op}(f)$ is the corresponding operator, then $\mathfrak{Op}(f)$ maps the Schwartz class into itself and it defines an essentially selfadjoint operator on $L^2(\mathbb R^n)$. As a consequence, we provide detailed spectral information of $\mathfrak{Op}(f)$. A complete characterization of the classical constants of motion of the Harmonic Oscillator is given and we also show that they form an algebra with the Moyal product. We give some interesting examples and we analyze Weinstein average method within our framework.
