互补与坐标变换:伪厄密性与弱伪厄密性之间的映射

Samir Saidani, S. Yahiaoui
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引用次数: 0

摘要

本文研究了由Bagchi和Quesne在《物理学》中提出的互补概念。列托人。[j] .中国科学:地球科学[j], vol . 17(2002)],当系统具有位置相关质量时,坐标变换的伪厄米性和弱伪厄米性。在修正动量下,我们首先确定了在伪厄米性的两个概念下识别复化势的生成函数$V_\pm(x)$。弱伪厄密性$\ widdetilde \eta_-$)。我们证明了互补的概念可以被理解和解释为通过它们各自的生成函数的坐标变换。从而得到了实现坐标变换的相似变换。我们证明了相似性变换被建立为连接$\ widdetilde \eta_+$和$\ widdetilde \eta_-$的基本关系。讨论了恒定质量下的一个特殊分解$\eta_+=\eta_-^\dagger \eta_-$,并推导了一些B\ \ acklund变换。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Complementarity vs coordinate transformations: Mapping between pseudo-Hermiticity and weak pseudo-Hermiticity
\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 $\widetilde\eta_+$ (resp. weak pseudo-Hermiticity $\widetilde\eta_-$). 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 $\widetilde\eta_+$ and $\widetilde\eta_-$. A special factorization $\eta_+=\eta_-^\dagger \eta_-$ is discussed in the case of a constant mass and some B\"acklund transformations are derived.
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