We point out the connection between the problem of formulating quantum mechanics in phase space and projecting the motion of a quantum mechanical particle onto a particular Landau level. In particular, we show that lowest Landau level wave functions, which are widely used in studies of quantum Hall effect, are actually phase space wave functions in this context. We demonstrate the usefulness of this understanding by analyzing some simple problems, and propose other utilities.

中文翻译：

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相空间量子力学作为Landau级问题

我们指出了在相空间中制定量子力学与将量子力学粒子的运动投影到特定的朗道能级之间的联系。特别地，我们证明了在这种情况下，在量子霍尔效应研究中广泛使用的最低的Landau能级波函数实际上是相空间波函数。我们通过分析一些简单的问题来证明这种理解的有用性，并提出其他实用程序。