基于Galilei群单纯表示的非对易谐振子
The Noncommutative Harmonic Oscillator based in Simplectic Representation of Galilei Group
摘要：
在这项工作中，我们研究了伽利略群的辛酉表示。由此导出了相空间中的薛定谔方程。该形式基于星积的非对易结构，并以群论方法为指导，构造了相空间中的物理相容理论。该状态由与维格纳函数相关联的准概率振幅描述。作为应用，在相空间中研究了三维谐振子和非对易谐振子，并确定了这两种情况下的Wigner函数。
英文摘要：
In this work we study symplectic unitary representations for the Galilei group. As a consequence the Schrödinger equation is derived in phase space. The formalism is based on the non-commutative structure of the star-product, and using the group theory approach as a guide a physical consistent theory in phase space is constructed. The state is described by a quasi-probability amplitude that is in association with the Wigner function. The 3D harmonic oscillator and the noncommutative oscillator are studied in phase space as an application, and the Wigner function associated to both cases are determined.
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