论文标题
互补性与坐标转换：伪热度与虚弱的伪热映射
Complementarity versus coordinate transformations: mapping between pseudo-Hermiticity and weak pseudo-Hermiticity
论文作者
论文摘要
\ noindent我们研究了Bagchi和Quesne在[Phys。 Lett。 a {\ bf 301}，173（2002）]，在系统具有与位置相关的质量时，在严格的数学观点中，在伪用的数学观点中，在伪 - 伪弱的数学观点中。我们首先确定在修改的摩托车下，生成的功能在两个伪 - 热的概念$ \widetildeη_+$（rep.弱的伪 - 伪$ \wideTildeη_- $）下，识别复杂电势$ v_ \ pm（x）$。我们表明，互补性的概念可以通过各自的生成功能理解并解释为坐标转换。结果，获得了实现坐标转换的相似性转换。我们表明，相似性转换设置为基本关系，即连接$ \widetildeη_+$和$ \widetildeη_- $。在恒定质量的情况下，讨论了一个特殊的分解$η_+=η_-^\匕首η_-$。
\noindent We study the concept of the complementarity, introduced by Bagchi and Quesne in [Phys. Lett. A {\bf 301}, 173 (2002)], between pseudo-Hermiticity and weak pseudo-Hermiticity in a rigorous mathematical viewpoint of coordinate transformations when a system has a position-dependent mass. We first determine, under the modified-momentum, the generating functions identifying the complexified potentials $V_\pm(x)$ under both concepts of pseudo-Hermiticity $\widetildeη_+$ (resp. weak pseudo-Hermiticity $\widetildeη_-$). We show that the concept of complementarity can be understood and interpreted as a coordinate transformation through their respective generating functions. As consequence, a similarity transformation which implements coordinate transformations is obtained. We show that the similarity transformation is set up as fundamental relationship connecting both $\widetildeη_+$ and $\widetildeη_-$. A special factorization $η_+=η_-^\dagger η_-$ is discussed in the case of a constant mass and some Bäcklund transformations are derived.
